#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------

#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)

library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.3     ✓ purrr   0.3.4
## ✓ tibble  3.0.6     ✓ dplyr   1.0.4
## ✓ tidyr   1.1.2     ✓ stringr 1.4.0
## ✓ readr   1.3.1     ✓ forcats 0.5.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
library(haven)
library(readxl)
library(mmpack)

#' For ggplots
simple_theme <- theme(
  #aspect.ratio = 1,
  text  = element_text(family="Calibri",size = 12, color = 'black'),
  panel.spacing.y = unit(0,"cm"),
  panel.spacing.x = unit(0.25, "lines"),
  panel.grid.minor = element_line(color = "transparent"),
  panel.grid.major = element_line(color = "transparent"),
  panel.border=element_rect(fill = NA),
  panel.background=element_blank(),
  axis.ticks = element_line(colour = "black"),
  axis.text = element_text(color = "black", size=10),
  # legend.position = c(0.1,0.1),
  plot.margin=grid::unit(c(0,0,0,0), "mm"),
  legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation

set.seed(123)

1 Exploring the data set

The HS data set was previously used in the CEI paper (Martenies et al., 2019). In the original analysis, we used an exposure index based on the CalEnvironScreen tool. We observed lower birth weights and lower adiposity associated with higher index scores, driven largely by exposures to social indicators of health at the neighborhood level. Now, we are aiming to use methods for mixtures to try to identify which exposures are driving these association.

The complete data set for the birth weight outcome consists of n = 897 participants. This represents 77.93% of the original Healthy Start 1 cohort.

Of the 897 participants, 27% identify as Latina, 17% identify as Black, and 27% identify as another non-NHW race or ethnicity. The median age of mothers in this dataset is 28 years. 51% of babies born were male.

1.1 Effect of year on birth weight

The following examines whether there are trends in birth weight by year of birth.

plot(hs_data1$dob, hs_data1$birth_weight)
abline(lm(birth_weight ~ dob, data = hs_data1), col = "red")

Grouping birth weights by conception year doesn’t show much of a trend:

bw_trends_by_concept <- ggplot(data = hs_data1) +
  geom_boxplot(aes(x = concep_year, group = concep_year, y = birth_weight))
bw_trends_by_concept
## Warning: Removed 5 rows containing non-finite values (stat_boxplot).

1.2 Exposure data

We have included 20 exposures in our analysis.

These exposures are based on the census tract where each mother lived at the time of enrollment into Healthy Start. With the exception of air pollution (mean_pm and mean_o3) and temperature, these are based on long-term averages at for each census tract. For the air pollutants and temerature variables, we used the average pollution levels across each pregnancy (est. conception date to delivery date) estimated using ordinary kriging and monitoring data.

#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
            mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
            cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
            pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
  as.matrix()
head(X)
##       mean_pm  mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 8.483046 47.19072  51.81487       6.006276       43.30893
## [2,] 6.598608 50.05090  58.32885       7.281109       48.36432
## [3,] 7.454146 48.57052  58.01924      17.205991       31.67281
## [4,] 6.671239 50.06429  61.35590       6.842898       45.00359
## [5,] 7.122537 50.14275  59.28421       3.357792       28.16745
## [6,] 7.637453 47.03125  55.32825      10.743612       45.87564
##      mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,]          10128.4962   2827.538   729.2371          4829.780
## [2,]          10749.0359   1576.420  5239.2211          4417.792
## [3,]           9048.6468   3350.303  2992.2968          5211.871
## [4,]           4223.3434   3364.954  6998.1286          8921.318
## [5,]            858.7283   2923.811  3427.2247          7006.042
## [6,]          15603.9800   3364.200  3166.5395          4484.960
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]          7968.654    29116.58        1749.1256     275.2480     155.7767
## [2,]          3780.951    51044.30        7354.5310     279.6435     226.8038
## [3,]          7423.232    36079.21        4887.2996     221.0414     157.6974
## [4,]          9636.816    42235.78        3752.6399     203.8812     142.5368
## [5,]          6806.912    29145.98         729.7784     194.1983     101.0046
## [6,]          5265.285    43921.85        5870.6867     174.3361     120.3281
##      violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,]          14.377133            37.32935   31.784946 11.529628
## [2,]           8.905404            67.03932   15.290231  4.908306
## [3,]           7.636888            46.78194    6.891702  4.564963
## [4,]           2.850212            21.95270    2.725915  5.623583
## [5,]           5.435988            22.49834   12.919186  5.234103
## [6,]           5.035971            47.15500    3.842365 10.000000
##      pct_limited_eng pct_hh_pov  pct_poc
## [1,]       26.114650  12.010919 90.33703
## [2,]        8.500401  18.123496 30.44025
## [3,]        0.000000   6.307978 26.63305
## [4,]        1.350621   9.292274 32.68648
## [5,]        6.307385   2.115768 73.60772
## [6,]        5.121799  25.171768 23.08698

Variance and histograms of the exposure variables (in their original units):

var(X)
##                             mean_pm        mean_o3     mean_temp pct_tree_cover
## mean_pm                 0.391784015    0.006083605    0.09741867     -0.2054297
## mean_o3                 0.006083605    9.383489039   11.72688428     -0.4158151
## mean_temp               0.097418667   11.726884276   20.59970005      0.4425544
## pct_tree_cover         -0.205429726   -0.415815089    0.44255440      9.7193077
## pct_impervious          0.508898445   -1.674151031    3.35723856      5.8719893
## mean_aadt_intensity  -182.234953786  474.627052967 2674.12174077   8431.6446632
## dist_m_tri           -255.176839682  444.286548683 -627.63132786    -73.1423054
## dist_m_npl           -289.002141382  539.849185829 -165.00509261    434.4654007
## dist_m_waste_site    -275.262105884  261.902915064   58.19389166   1933.8647304
## dist_m_major_emit      71.096593638  577.257325397  138.98687089    265.4284518
## dist_m_cafo         -1291.237441927  -35.275020052  237.89751842  10170.6234275
## dist_m_mine_well     -339.250592215 -375.434990683 -202.34883778   3136.3680766
## cvd_rate_adj            3.871688575    0.939328342    7.31791796    -24.8232924
## res_rate_adj            2.356328835   -0.181515705    7.98167422     -3.5331376
## violent_crime_rate      0.232839920    0.577648302    1.07794996     -4.0583754
## property_crime_rate     2.001989749   -2.773092354    6.06649992    -22.6429724
## pct_less_hs             1.132232861    0.637361326    0.69410116     -7.5753471
## pct_unemp               0.100439902    0.288530482    0.25729682     -0.3330523
## pct_limited_eng         0.432516169    0.295617023    0.05811301     -2.8349116
## pct_hh_pov              0.731824476   -0.606648513    0.73475917      0.3805472
## pct_poc                 1.632059580    1.202932299   -0.90133106    -19.4091792
##                     pct_impervious mean_aadt_intensity     dist_m_tri
## mean_pm                  0.5088984           -182.2350     -255.17684
## mean_o3                 -1.6741510            474.6271      444.28655
## mean_temp                3.3572386           2674.1217     -627.63133
## pct_tree_cover           5.8719893           8431.6447      -73.14231
## pct_impervious         176.8316214          55459.6063   -15279.44024
## mean_aadt_intensity  55459.6063235       67283287.0201 -1315386.69307
## dist_m_tri          -15279.4402428       -1315386.6931  6558190.20296
## dist_m_npl           -7729.3843793        1683196.0799  4282727.94125
## dist_m_waste_site    -4662.9983638        2039577.9230  2441267.84540
## dist_m_major_emit     2627.0270993        2477155.3406  1433153.16531
## dist_m_cafo          16586.9964129       15462371.9832  3431065.70215
## dist_m_mine_well       706.6674650        2073244.5987   995872.11873
## cvd_rate_adj           230.4542985          20477.4374   -49347.60273
## res_rate_adj           176.8108084          33055.3733   -31870.98664
## violent_crime_rate      26.6945028           5736.5627    -1014.08753
## property_crime_rate    118.0737725          22077.3894    -5365.69285
## pct_less_hs             56.8383947          -4056.6889   -12372.14262
## pct_unemp               25.9434246           6003.3343    -2527.22451
## pct_limited_eng         41.9919053           2620.6198    -5408.86434
## pct_hh_pov              82.2198624          17850.1649    -8842.76408
## pct_poc                 88.3560154           4526.2710   -18049.42332
##                        dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm                 -289.0021        -275.26211          71.09659
## mean_o3                  539.8492         261.90292         577.25733
## mean_temp               -165.0051          58.19389         138.98687
## pct_tree_cover           434.4654        1933.86473         265.42845
## pct_impervious         -7729.3844       -4662.99836        2627.02710
## mean_aadt_intensity  1683196.0799     2039577.92299     2477155.34057
## dist_m_tri           4282727.9413     2441267.84540     1433153.16531
## dist_m_npl          11125411.7474     4193498.05859     6948817.25739
## dist_m_waste_site    4193498.0586     5344101.75397     1395277.06805
## dist_m_major_emit    6948817.2574     1395277.06805    10114549.72263
## dist_m_cafo          5416531.1320     5586018.82514    -2993791.05377
## dist_m_mine_well      256924.3029     1375784.78556    -1810174.74785
## cvd_rate_adj          -30921.0390      -43119.57852       16272.40152
## res_rate_adj          -19393.1304      -32402.84395       -1320.21297
## violent_crime_rate      -672.9264       -3702.61118        -360.49700
## property_crime_rate   -18283.4264      -22350.30055      -24007.42305
## pct_less_hs            -6760.5337      -11422.49855        8866.74917
## pct_unemp               2195.0515       -1476.40942        5212.74830
## pct_limited_eng          498.0033       -4277.81339        9367.28435
## pct_hh_pov             -1135.3843       -7599.74324        8682.26135
## pct_poc                -1456.8941       -8602.85207       22698.24353
##                        dist_m_cafo dist_m_mine_well   cvd_rate_adj
## mean_pm                -1291.23744        -339.2506      3.8716886
## mean_o3                  -35.27502        -375.4350      0.9393283
## mean_temp                237.89752        -202.3488      7.3179180
## pct_tree_cover         10170.62343        3136.3681    -24.8232924
## pct_impervious         16586.99641         706.6675    230.4542985
## mean_aadt_intensity 15462371.98316     2073244.5987  20477.4373759
## dist_m_tri           3431065.70215      995872.1187 -49347.6027339
## dist_m_npl           5416531.13199      256924.3029 -30921.0389720
## dist_m_waste_site    5586018.82514     1375784.7856 -43119.5785165
## dist_m_major_emit   -2993791.05377    -1810174.7478  16272.4015197
## dist_m_cafo         46324000.89481     9345575.3772 -46645.9665229
## dist_m_mine_well     9345575.37722     4430024.9964 -39046.5984701
## cvd_rate_adj          -46645.96652      -39046.5985   2039.8569530
## res_rate_adj          -13772.40263      -16322.5110   1289.5661935
## violent_crime_rate       722.31907       -2032.3464    135.9487143
## property_crime_rate   -15833.92381       -4272.3829    343.9364726
## pct_less_hs           -26060.83378      -10037.6577    328.3044447
## pct_unemp              -1030.96916       -2827.2369    105.0153846
## pct_limited_eng        -7089.15821       -4814.6687    183.5853966
## pct_hh_pov              -855.38016       -5030.4055    266.1004715
## pct_poc               -44526.37107      -24974.3303    618.2817294
##                       res_rate_adj violent_crime_rate property_crime_rate
## mean_pm                  2.3563288          0.2328399            2.001990
## mean_o3                 -0.1815157          0.5776483           -2.773092
## mean_temp                7.9816742          1.0779500            6.066500
## pct_tree_cover          -3.5331376         -4.0583754          -22.642972
## pct_impervious         176.8108084         26.6945028          118.073773
## mean_aadt_intensity  33055.3733277       5736.5627383        22077.389365
## dist_m_tri          -31870.9866403      -1014.0875345        -5365.692846
## dist_m_npl          -19393.1304345       -672.9263612       -18283.426420
## dist_m_waste_site   -32402.8439544      -3702.6111771       -22350.300554
## dist_m_major_emit    -1320.2129699       -360.4970006       -24007.423046
## dist_m_cafo         -13772.4026269        722.3190727       -15833.923813
## dist_m_mine_well    -16322.5110008      -2032.3464340        -4272.382880
## cvd_rate_adj          1289.5661935        135.9487143          343.936473
## res_rate_adj          1091.1856742        104.4979610          333.780710
## violent_crime_rate     104.4979610         40.1175363          160.725724
## property_crime_rate    333.7807097        160.7257236         1295.004010
## pct_less_hs            197.8827546         22.5579950           -3.138375
## pct_unemp               72.3576933         11.3130282            1.362247
## pct_limited_eng        104.0524036         12.7978322          -14.963510
## pct_hh_pov             201.6582659         29.1947400           64.236239
## pct_poc                297.8399442         46.4013012          -44.321973
##                        pct_less_hs     pct_unemp pct_limited_eng    pct_hh_pov
## mean_pm                  1.1322329     0.1004399      0.43251617     0.7318245
## mean_o3                  0.6373613     0.2885305      0.29561702    -0.6066485
## mean_temp                0.6941012     0.2572968      0.05811301     0.7347592
## pct_tree_cover          -7.5753471    -0.3330523     -2.83491161     0.3805472
## pct_impervious          56.8383947    25.9434246     41.99190527    82.2198624
## mean_aadt_intensity  -4056.6889048  6003.3343312   2620.61975287 17850.1649192
## dist_m_tri          -12372.1426191 -2527.2245090  -5408.86433682 -8842.7640785
## dist_m_npl           -6760.5337115  2195.0514738    498.00334199 -1135.3843390
## dist_m_waste_site   -11422.4985495 -1476.4094188  -4277.81339346 -7599.7432386
## dist_m_major_emit     8866.7491706  5212.7483023   9367.28434718  8682.2613524
## dist_m_cafo         -26060.8337755 -1030.9691591  -7089.15821141  -855.3801591
## dist_m_mine_well    -10037.6576614 -2827.2368665  -4814.66874000 -5030.4055237
## cvd_rate_adj           328.3044447   105.0153846    183.58539661   266.1004715
## res_rate_adj           197.8827546    72.3576933    104.05240356   201.6582659
## violent_crime_rate      22.5579950    11.3130282     12.79783224    29.1947400
## property_crime_rate     -3.1383751     1.3622468    -14.96351049    64.2362387
## pct_less_hs            162.1681017    39.4206217     85.19100137   100.9072175
## pct_unemp               39.4206217    24.6546969     25.21727694    36.9693212
## pct_limited_eng         85.1910014    25.2172769     68.65329426    67.2758215
## pct_hh_pov             100.9072175    36.9693212     67.27582153   119.7157808
## pct_poc                238.8801445    72.7999599    142.19618383   155.4992975
##                            pct_poc
## mean_pm                  1.6320596
## mean_o3                  1.2029323
## mean_temp               -0.9013311
## pct_tree_cover         -19.4091792
## pct_impervious          88.3560154
## mean_aadt_intensity   4526.2710457
## dist_m_tri          -18049.4233248
## dist_m_npl           -1456.8941447
## dist_m_waste_site    -8602.8520680
## dist_m_major_emit    22698.2435288
## dist_m_cafo         -44526.3710716
## dist_m_mine_well    -24974.3303024
## cvd_rate_adj           618.2817294
## res_rate_adj           297.8399442
## violent_crime_rate      46.4013012
## property_crime_rate    -44.3219731
## pct_less_hs            238.8801445
## pct_unemp               72.7999599
## pct_limited_eng        142.1961838
## pct_hh_pov             155.4992975
## pct_poc                524.7591044
ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Scaling the exposure variables

X.scaled <- apply(X, 2, scale)
head(X.scaled)
##          mean_pm    mean_o3  mean_temp pct_tree_cover pct_impervious
## [1,]  1.60876944 -0.2502907 -0.1690421    -0.08261827      0.2084897
## [2,] -1.40186806  0.6834152  1.2661699     0.32629926      0.5886571
## [3,] -0.03503482  0.2001460  1.1979551     3.50981981     -0.6665506
## [4,] -1.28583023  0.6877893  1.9331141     0.18573791      0.3359288
## [5,] -0.56482237  0.7133998  1.4766616    -0.93215008     -0.9301550
## [6,]  0.25782234 -0.3023500  0.6050531     1.43693690      0.4015075
##      mean_aadt_intensity dist_m_tri  dist_m_npl dist_m_waste_site
## [1,]         -0.02626143 -0.4008664 -1.44212141      -0.172775897
## [2,]          0.04938980 -0.8894134 -0.08999604      -0.350992130
## [3,]         -0.15790801 -0.1967327 -0.76363997      -0.007492447
## [4,]         -0.74617032 -0.1910117  0.43733697       1.597126043
## [5,]         -1.15635722 -0.3632728 -0.63324550       0.768623456
## [6,]          0.64126566 -0.1913062 -0.71140077      -0.321936759
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]        -0.1090638  -1.1354079       -0.7748959    0.6917151   -0.2847192
## [2,]        -1.4258114   2.0863310        1.8883051    0.7890362    1.8654606
## [3,]        -0.2805619  -0.1124210        0.7160914   -0.5084805   -0.2265752
## [4,]         0.4154599   0.7921355        0.1769998   -0.8884275   -0.6855261
## [5,]        -0.4743524  -1.1310891       -1.2592010   -1.1028189   -1.9428184
## [6,]        -0.9590895   1.0398621        1.1833114   -1.5425892   -1.3578439
##      violent_crime_rate property_crime_rate pct_less_hs   pct_unemp
## [1,]          0.2444833          -0.5008789  1.20091488  0.36793456
## [2,]         -0.6194047           0.3247153 -0.09436047 -0.96557105
## [3,]         -0.8196807          -0.2382061 -0.75386917 -1.03471894
## [4,]         -1.5754111          -0.9281724 -1.08099463 -0.82151747
## [5,]         -1.1671633          -0.9130100 -0.28055077 -0.89995692
## [6,]         -1.2303189          -0.2278392 -0.99332353  0.05987409
##      pct_limited_eng pct_hh_pov    pct_poc
## [1,]      2.15383825 -0.3020187  1.5727240
## [2,]      0.02798425  0.2566428 -1.0419857
## [3,]     -0.99792447 -0.8232412 -1.2081839
## [4,]     -0.83491873 -0.5504902 -0.9439299
## [5,]     -0.23668961 -1.2063898  0.8424295
## [6,]     -0.37977738  0.9008223 -1.3629822

Variance and histograms of the exposure variables (scaled):

var(X.scaled)
##                          mean_pm      mean_o3    mean_temp pct_tree_cover
## mean_pm              1.000000000  0.003172893  0.034291650   -0.105274276
## mean_o3              0.003172893  1.000000000  0.843470729   -0.043541201
## mean_temp            0.034291650  0.843470729  1.000000000    0.031276529
## pct_tree_cover      -0.105274276 -0.043541201  0.031276529    1.000000000
## pct_impervious       0.061140333 -0.041099117  0.055625226    0.141640558
## mean_aadt_intensity -0.035493982  0.018889337  0.071828554    0.329716765
## dist_m_tri          -0.159193706  0.056635532 -0.053998558   -0.009161339
## dist_m_npl          -0.138426634  0.052836279 -0.010899557    0.041781063
## dist_m_waste_site   -0.190232937  0.036984589  0.005546380    0.268331135
## dist_m_major_emit    0.035715124  0.059253499  0.009628753    0.026770503
## dist_m_cafo         -0.303095664 -0.001691929  0.007701165    0.479321466
## dist_m_mine_well    -0.257510042 -0.058230361 -0.021182010    0.477976199
## cvd_rate_adj         0.136954783  0.006789463  0.035699097   -0.176295758
## res_rate_adj         0.113962827 -0.001793836  0.053237079   -0.034307854
## violent_crime_rate   0.058730941  0.029772424  0.037497389   -0.205526308
## property_crime_rate  0.088879773 -0.025156291  0.037142591   -0.201827442
## pct_less_hs          0.142046220  0.016338825  0.012009076   -0.190810449
## pct_unemp            0.032317153  0.018969666  0.011417056   -0.021515177
## pct_limited_eng      0.083396591  0.011647067  0.001545298   -0.109746623
## pct_hh_pov           0.106858205 -0.018100029  0.014795814    0.011156172
## pct_poc              0.113823690  0.017142692 -0.008669098   -0.271775006
##                     pct_impervious mean_aadt_intensity   dist_m_tri  dist_m_npl
## mean_pm                 0.06114033         -0.03549398 -0.159193706 -0.13842663
## mean_o3                -0.04109912          0.01888934  0.056635532  0.05283628
## mean_temp               0.05562523          0.07182855 -0.053998558 -0.01089956
## pct_tree_cover          0.14164056          0.32971677 -0.009161339  0.04178106
## pct_impervious          1.00000000          0.50844411 -0.448678724 -0.17426369
## mean_aadt_intensity     0.50844411          1.00000000 -0.062619247  0.06152095
## dist_m_tri             -0.44867872         -0.06261925  1.000000000  0.50138396
## dist_m_npl             -0.17426369          0.06152095  0.501383960  1.00000000
## dist_m_waste_site      -0.15168685          0.10755964  0.412369055  0.54385239
## dist_m_major_emit       0.06211712          0.09495686  0.175965418  0.65505772
## dist_m_cafo             0.18326720          0.27696155  0.196849357  0.23859436
## dist_m_mine_well        0.02524829          0.12008641  0.184760224  0.03659688
## cvd_rate_adj            0.38371166          0.05527416 -0.426652406 -0.20525615
## res_rate_adj            0.40251263          0.12199419 -0.376750794 -0.17601130
## violent_crime_rate      0.31693831          0.11041575 -0.062519618 -0.03185242
## property_crime_rate     0.24673907          0.07479259 -0.058223492 -0.15232247
## pct_less_hs             0.33564418         -0.03883608 -0.379376300 -0.15916230
## pct_unemp               0.39291400          0.14739715 -0.198747643  0.13253691
## pct_limited_eng         0.38111402          0.03855846 -0.254907958  0.01801953
## pct_hh_pov              0.56509450          0.19888999 -0.315587892 -0.03111065
## pct_poc                 0.29005220          0.02408835 -0.307674381 -0.01906733
##                     dist_m_waste_site dist_m_major_emit  dist_m_cafo
## mean_pm                   -0.19023294       0.035715124 -0.303095664
## mean_o3                    0.03698459       0.059253499 -0.001691929
## mean_temp                  0.00554638       0.009628753  0.007701165
## pct_tree_cover             0.26833114       0.026770503  0.479321466
## pct_impervious            -0.15168685       0.062117120  0.183267205
## mean_aadt_intensity        0.10755964       0.094956864  0.276961553
## dist_m_tri                 0.41236906       0.175965418  0.196849357
## dist_m_npl                 0.54385239       0.655057717  0.238594356
## dist_m_waste_site          1.00000000       0.189779728  0.355027509
## dist_m_major_emit          0.18977973       1.000000000 -0.138307324
## dist_m_cafo                0.35502751      -0.138307324  1.000000000
## dist_m_mine_well           0.28275484      -0.270423318  0.652378929
## cvd_rate_adj              -0.41298787       0.113286594 -0.151743889
## res_rate_adj              -0.42432287      -0.012566704 -0.061257230
## violent_crime_rate        -0.25287368      -0.017896218  0.016755559
## property_crime_rate       -0.26866460      -0.209766780 -0.064647236
## pct_less_hs               -0.38800832       0.218931589 -0.300678627
## pct_unemp                 -0.12862329       0.330098571 -0.030506530
## pct_limited_eng           -0.22333346       0.355475551 -0.125707430
## pct_hh_pov                -0.30045944       0.249507656 -0.011486308
## pct_poc                   -0.16245202       0.311558055 -0.285584268
##                     dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm                  -0.25751004  0.136954783  0.113962827
## mean_o3                  -0.05823036  0.006789463 -0.001793836
## mean_temp                -0.02118201  0.035699097  0.053237079
## pct_tree_cover            0.47797620 -0.176295758 -0.034307854
## pct_impervious            0.02524829  0.383711656  0.402512635
## mean_aadt_intensity       0.12008641  0.055274160  0.121994187
## dist_m_tri                0.18476022 -0.426652406 -0.376750794
## dist_m_npl                0.03659688 -0.205256148 -0.176011297
## dist_m_waste_site         0.28275484 -0.412987865 -0.424322872
## dist_m_major_emit        -0.27042332  0.113286594 -0.012566704
## dist_m_cafo               0.65237893 -0.151743889 -0.061257230
## dist_m_mine_well          1.00000000 -0.410752544 -0.234765650
## cvd_rate_adj             -0.41075254  1.000000000  0.864359590
## res_rate_adj             -0.23476565  0.864359590  1.000000000
## violent_crime_rate       -0.15245003  0.475234675  0.499449246
## property_crime_rate      -0.05640681  0.211613232  0.280786581
## pct_less_hs              -0.37449548  0.570813439  0.470409304
## pct_unemp                -0.27052616  0.468277441  0.441149256
## pct_limited_eng          -0.27607853  0.490577454  0.380164971
## pct_hh_pov               -0.21843600  0.538480631  0.557944498
## pct_poc                  -0.51797735  0.597594464  0.393598671
##                     violent_crime_rate property_crime_rate pct_less_hs
## mean_pm                     0.05873094         0.088879773  0.14204622
## mean_o3                     0.02977242        -0.025156291  0.01633882
## mean_temp                   0.03749739         0.037142591  0.01200908
## pct_tree_cover             -0.20552631        -0.201827442 -0.19081045
## pct_impervious              0.31693831         0.246739067  0.33564418
## mean_aadt_intensity         0.11041575         0.074792588 -0.03883608
## dist_m_tri                 -0.06251962        -0.058223492 -0.37937630
## dist_m_npl                 -0.03185242        -0.152322474 -0.15916230
## dist_m_waste_site          -0.25287368        -0.268664603 -0.38800832
## dist_m_major_emit          -0.01789622        -0.209766780  0.21893159
## dist_m_cafo                 0.01675556        -0.064647236 -0.30067863
## dist_m_mine_well           -0.15245003        -0.056406808 -0.37449548
## cvd_rate_adj                0.47523468         0.211613232  0.57081344
## res_rate_adj                0.49944925         0.280786581  0.47040930
## violent_crime_rate          1.00000000         0.705151942  0.27967307
## property_crime_rate         0.70515194         1.000000000 -0.00684836
## pct_less_hs                 0.27967307        -0.006848360  1.00000000
## pct_unemp                   0.35971778         0.007623781  0.62343462
## pct_limited_eng             0.24385889        -0.050184228  0.80738433
## pct_hh_pov                  0.42127121         0.163143151  0.72420883
## pct_poc                     0.31980337        -0.053765481  0.81887450
##                        pct_unemp pct_limited_eng  pct_hh_pov      pct_poc
## mean_pm              0.032317153     0.083396591  0.10685820  0.113823690
## mean_o3              0.018969666     0.011647067 -0.01810003  0.017142692
## mean_temp            0.011417056     0.001545298  0.01479581 -0.008669098
## pct_tree_cover      -0.021515177    -0.109746623  0.01115617 -0.271775006
## pct_impervious       0.392914001     0.381114020  0.56509450  0.290052202
## mean_aadt_intensity  0.147397153     0.038558463  0.19888999  0.024088345
## dist_m_tri          -0.198747643    -0.254907958 -0.31558789 -0.307674381
## dist_m_npl           0.132536906     0.018019533 -0.03111065 -0.019067333
## dist_m_waste_site   -0.128623290    -0.223333456 -0.30045944 -0.162452016
## dist_m_major_emit    0.330098571     0.355475551  0.24950766  0.311558055
## dist_m_cafo         -0.030506530    -0.125707430 -0.01148631 -0.285584268
## dist_m_mine_well    -0.270526163    -0.276078529 -0.21843600 -0.517977353
## cvd_rate_adj         0.468277441     0.490577454  0.53848063  0.597594464
## res_rate_adj         0.441149256     0.380164971  0.55794450  0.393598671
## violent_crime_rate   0.359717785     0.243858891  0.42127121  0.319803374
## property_crime_rate  0.007623781    -0.050184228  0.16314315 -0.053765481
## pct_less_hs          0.623434625     0.807384330  0.72420883  0.818874497
## pct_unemp            1.000000000     0.612939575  0.68048090  0.640031449
## pct_limited_eng      0.612939575     1.000000000  0.74208323  0.749164620
## pct_hh_pov           0.680480902     0.742083231  1.00000000  0.620401357
## pct_poc              0.640031449     0.749164620  0.62040136  1.000000000
ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.3 Covariate data

Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.

W <- select(hs_data2, 
            lat, lon, lat_lon_int,
            latina_re, black_re, other_re,
            ed_no_hs, ed_hs, ed_aa, ed_4yr,
            low_bmi, ovwt_bmi, obese_bmi,
            concep_spring, concep_summer, concep_fall,
            concep_2010, concep_2011, concep_2012, concep_2013,
            maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
            male, gest_age_w) %>%
  as.matrix()
head(W)
##           lat       lon lat_lon_int latina_re black_re other_re ed_no_hs ed_hs
## [1,] 39.79402 -104.8133   -4170.944         1        0        0        0     0
## [2,] 39.62671 -104.9927   -4160.517         0        0        1        0     0
## [3,] 39.74934 -104.9129   -4170.219         0        0        0        0     0
## [4,] 39.68397 -104.8933   -4162.583         0        0        0        0     0
## [5,] 39.79134 -104.7669   -4168.814         0        1        0        0     0
## [6,] 39.68050 -104.9451   -4164.274         1        0        0        0     0
##      ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,]     1      0       0        0         0             0             0
## [2,]     1      0       0        0         0             0             0
## [3,]     0      0       0        0         0             0             0
## [4,]     1      0       0        0         0             1             0
## [5,]     0      1       0        0         0             1             0
## [6,]     1      0       0        0         0             0             0
##      concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,]           0           0           0           0           0           19
## [2,]           0           1           0           0           0           36
## [3,]           0           1           0           0           0           34
## [4,]           0           1           0           0           0           28
## [5,]           0           1           0           0           0           30
## [6,]           0           1           0           0           0           22
##      any_smoker smokeSH mean_cpss mean_epsd male gest_age_w
## [1,]          0       1        29         0    0   40.57143
## [2,]          0       0        19         2    1   35.85714
## [3,]          0       0        19         1    0   40.42857
## [4,]          0       0        20         0    0   36.28571
## [5,]          0       0        15         0    1   38.42857
## [6,]          0       0        17         1    0   40.71429

Scaled the non-binary (continuous) covariates

colnames(W)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"          "gest_age_w"
W.s <- apply(W[,c(1, 2, 3, 21, 24, 25, 27)], 2, scale) #' just the continuous ones

W.scaled <- cbind(W.s[,1:3],
                  W[,4:20], W.s[,4],
                  W[,22:23], W.s[,5:6],
                  W[,26], W.s[,7])
colnames(W.scaled)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] ""              "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     ""              ""
colnames(W.scaled) <- colnames(W)
head(W.scaled)
##             lat        lon lat_lon_int latina_re black_re other_re ed_no_hs
## [1,]  0.9587536  0.5410850  -0.5821980         1        0        0        0
## [2,] -1.5498523 -1.6236392   0.6519093         0        0        1        0
## [3,]  0.2887793 -0.6606299  -0.4964164         0        0        0        0
## [4,] -0.6913627 -0.4239607   0.4073829         0        0        0        0
## [5,]  0.9185421  1.1019032  -0.3300513         0        1        0        0
## [6,] -0.7433125 -1.0489343   0.2071583         1        0        0        0
##      ed_hs ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,]     0     1      0       0        0         0             0             0
## [2,]     0     1      0       0        0         0             0             0
## [3,]     0     0      0       0        0         0             0             0
## [4,]     0     1      0       0        0         0             1             0
## [5,]     0     0      1       0        0         0             1             0
## [6,]     0     1      0       0        0         0             0             0
##      concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,]           0           0           0           0           0  -1.39815187
## [2,]           0           1           0           0           0   1.35109608
## [3,]           0           1           0           0           0   1.02765515
## [4,]           0           1           0           0           0   0.05733234
## [5,]           0           1           0           0           0   0.38077328
## [6,]           0           1           0           0           0  -0.91299047
##      any_smoker smokeSH  mean_cpss  mean_epsd male gest_age_w
## [1,]          0       1  3.3147856 -1.2832098    0  0.7037686
## [2,]          0       0  0.1179652 -0.6860171    1 -1.9146645
## [3,]          0       0  0.1179652 -0.9846134    0  0.6244221
## [4,]          0       0  0.4376472 -1.2832098    0 -1.6766251
## [5,]          0       0 -1.1607630 -1.2832098    1 -0.4864283
## [6,]          0       0 -0.5213989 -0.9846134    0  0.7831150
summary(W.scaled)
##       lat                lon           lat_lon_int         latina_re     
##  Min.   :-2.45418   Min.   :-2.5043   Min.   :-3.48430   Min.   :0.0000  
##  1st Qu.:-0.62577   1st Qu.:-0.5848   1st Qu.:-0.48738   1st Qu.:0.0000  
##  Median : 0.03151   Median : 0.1214   Median : 0.02121   Median :0.0000  
##  Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.00000   Mean   :0.2653  
##  3rd Qu.: 0.42402   3rd Qu.: 0.6654   3rd Qu.: 0.60627   3rd Qu.:1.0000  
##  Max.   : 4.00304   Max.   : 4.5531   Max.   : 2.60273   Max.   :1.0000  
##     black_re         other_re          ed_no_hs          ed_hs       
##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.00000   Median :0.0000   Median :0.0000  
##  Mean   :0.1717   Mean   :0.06689   Mean   :0.1527   Mean   :0.1851  
##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.00000   Max.   :1.0000   Max.   :1.0000  
##      ed_aa            ed_4yr          low_bmi           ovwt_bmi    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.000  
##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.000  
##  Mean   :0.2319   Mean   :0.2185   Mean   :0.03344   Mean   :0.262  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:1.000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.000  
##    obese_bmi      concep_spring    concep_summer     concep_fall    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.1996   Mean   :0.2497   Mean   :0.2408   Mean   :0.2709  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   concep_2010      concep_2011      concep_2012      concep_2013    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.1616   Mean   :0.3021   Mean   :0.2932   Mean   :0.2419  
##  3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   maternal_age        any_smoker         smokeSH         mean_cpss      
##  Min.   :-1.88331   Min.   :0.00000   Min.   :0.0000   Min.   :-5.9560  
##  1st Qu.:-0.91299   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:-0.5214  
##  Median : 0.05733   Median :0.00000   Median :0.0000   Median : 0.0114  
##  Mean   : 0.00000   Mean   :0.08696   Mean   :0.2575   Mean   : 0.0000  
##  3rd Qu.: 0.70421   3rd Qu.:0.00000   3rd Qu.:1.0000   3rd Qu.: 0.5442  
##  Max.   : 2.64486   Max.   :1.00000   Max.   :1.0000   Max.   : 4.5935  
##    mean_epsd            male          gest_age_w     
##  Min.   :-1.2832   Min.   :0.0000   Min.   :-7.7070  
##  1st Qu.:-0.7855   1st Qu.:0.0000   1st Qu.:-0.3277  
##  Median :-0.1884   Median :1.0000   Median : 0.1483  
##  Mean   : 0.0000   Mean   :0.5117   Mean   : 0.0000  
##  3rd Qu.: 0.6079   3rd Qu.:1.0000   3rd Qu.: 0.6244  
##  Max.   : 6.0324   Max.   :1.0000   Max.   : 2.9255

Variance and histograms for the scaled covariates

var(W.scaled)
##                         lat            lon   lat_lon_int      latina_re
## lat            1.0000000000 -0.25261855699 -0.9261702843  0.02075377736
## lon           -0.2526185570  1.00000000000  0.5988415501  0.01061991294
## lat_lon_int   -0.9261702843  0.59884155012  1.0000000000 -0.01302007756
## latina_re      0.0207537774  0.01061991294 -0.0130200776  0.19514701784
## black_re      -0.0122649034  0.04784916212  0.0288174353 -0.04560340022
## other_re      -0.0009403195 -0.00123694771  0.0002902002 -0.01776755853
## ed_no_hs       0.0058668471  0.01732912905  0.0019047436  0.03978788422
## ed_hs         -0.0130652792  0.04117136599  0.0268694085  0.02896808807
## ed_aa         -0.0071789427  0.04676104709  0.0241824221  0.01318258282
## ed_4yr         0.0022352364 -0.00766878563 -0.0048607788 -0.03571926262
## low_bmi       -0.0029774584 -0.00003551643  0.0024531145  0.00004479216
## ovwt_bmi       0.0205880066  0.00512460048 -0.0150602639  0.02081218148
## obese_bmi      0.0165669344  0.00976713009 -0.0098964732  0.02065416468
## concep_spring  0.0143292896 -0.00046075172 -0.0120393632 -0.00606436136
## concep_summer -0.0140319053 -0.00711327850  0.0088444045 -0.00481142499
## concep_fall    0.0054905592  0.01642183233  0.0018457750  0.01732710225
## concep_2010    0.0110681241  0.00844610317 -0.0058861055 -0.00610790930
## concep_2011   -0.0220635440  0.01869831001  0.0255410960 -0.00882156792
## concep_2012    0.0024435961 -0.00706763788 -0.0047707939  0.01252065416
## concep_2013    0.0074817863 -0.02068066481 -0.0142344221  0.00158887761
## maternal_age   0.0307789398 -0.17980907079 -0.0955945618 -0.10858833047
## any_smoker    -0.0082274331  0.02279799333  0.0156963705 -0.00858889752
## smokeSH       -0.0111042258  0.04668855425  0.0273846128 -0.00590510033
## mean_cpss     -0.0258360855 -0.01114736129  0.0170462313 -0.04668314421
## mean_epsd     -0.0347375477  0.05084465609  0.0485855489  0.04322362524
## male           0.0290047629 -0.02552947737 -0.0339519192 -0.00087717989
## gest_age_w     0.0111191604 -0.03926647196 -0.0245324539 -0.02639363168
##                    black_re      other_re      ed_no_hs          ed_hs
## lat           -0.0122649034 -0.0009403195  0.0058668471 -0.01306527915
## lon            0.0478491621 -0.0012369477  0.0173291290  0.04117136599
## lat_lon_int    0.0288174353  0.0002902002  0.0019047436  0.02686940852
## latina_re     -0.0456034002 -0.0177675585  0.0397878842  0.02896808807
## black_re       0.1423669175 -0.0114966555  0.0128118032  0.01506758640
## other_re      -0.0114966555  0.0624850693 -0.0035311156  0.00658071548
## ed_no_hs       0.0128118032 -0.0035311156  0.1295488931 -0.02829620561
## ed_hs          0.0150675864  0.0065807155 -0.0282962056  0.15098194378
## ed_aa          0.0192967133  0.0023291925 -0.0354554865 -0.04296066253
## ed_4yr        -0.0163503842 -0.0034713927 -0.0334099777 -0.04048216276
## low_bmi        0.0020641722 -0.0011235368 -0.0039977007 -0.00173196369
## ovwt_bmi      -0.0003857103 -0.0052668120  0.0045849757 -0.00612657270
## obese_bmi      0.0069962872  0.0022620043  0.0063181836  0.02441297380
## concep_spring  0.0017220099  0.0044829491 -0.0002364031  0.00395788541
## concep_summer -0.0079058170  0.0017319637 -0.0044530877 -0.00331835284
## concep_fall   -0.0063828834 -0.0047479694  0.0110338032  0.00226573698
## concep_2010    0.0090467730 -0.0007801302 -0.0001629937  0.00576574693
## concep_2011    0.0183859392 -0.0023739847  0.0096091635 -0.00463350056
## concep_2012   -0.0146793876  0.0004553870 -0.0035360925  0.00371526119
## concep_2013   -0.0125617136  0.0027733815 -0.0057396182 -0.00464096592
## maternal_age  -0.0895968722 -0.0133074822 -0.1376124653 -0.10868310364
## any_smoker     0.0185364907 -0.0013586957  0.0179541925  0.00174689441
## smokeSH        0.0349789477  0.0084246596  0.0309364548  0.02483352246
## mean_cpss     -0.0233123370  0.0255604593 -0.0561153540 -0.03433895561
## mean_epsd      0.0220578552  0.0202679881  0.0670107276  0.02014619096
## male           0.0002202281  0.0003322086 -0.0135085702  0.00006345557
## gest_age_w    -0.0368471269 -0.0054750903 -0.0076928484 -0.01723767893
##                      ed_aa        ed_4yr        low_bmi      ovwt_bmi
## lat           -0.007178943  0.0022352364 -0.00297745845  0.0205880066
## lon            0.046761047 -0.0076687856 -0.00003551643  0.0051246005
## lat_lon_int    0.024182422 -0.0048607788  0.00245311454 -0.0150602639
## latina_re      0.013182583 -0.0357192626  0.00004479216  0.0208121815
## black_re       0.019296713 -0.0163503842  0.00206417224 -0.0003857103
## other_re       0.002329193 -0.0034713927 -0.00112353679 -0.0052668120
## ed_no_hs      -0.035455487 -0.0334099777 -0.00399770067  0.0045849757
## ed_hs         -0.042960663 -0.0404821628 -0.00173196369 -0.0061265727
## ed_aa          0.178312629 -0.0507246377  0.00786102484  0.0150750518
## ed_4yr        -0.050724638  0.1709517837 -0.00173569637  0.0040748427
## low_bmi        0.007861025 -0.0017356964  0.03236233875 -0.0087717989
## ovwt_bmi       0.015075052  0.0040748427 -0.00877179885  0.1935643614
## obese_bmi      0.009478520 -0.0124024526 -0.00668149785 -0.0523383998
## concep_spring  0.006761128 -0.0066354615 -0.00501298973  0.0092806876
## concep_summer -0.011257764  0.0064762004  0.00309812470 -0.0051212375
## concep_fall   -0.007084627  0.0010078237  0.00320637243  0.0026091436
## concep_2010    0.004884834  0.0003533604  0.00128404204 -0.0033345278
## concep_2011    0.002410067  0.0053402214  0.00439336479  0.0055828456
## concep_2012   -0.005564182 -0.0061016882 -0.00535266364 -0.0043547938
## concep_2013   -0.002587992  0.0006519748 -0.00028741639  0.0023988692
## maternal_age  -0.040296710  0.1091044519 -0.01089529356  0.0089002276
## any_smoker     0.011063665 -0.0156735248  0.00155279503 -0.0060656056
## smokeSH        0.022806677 -0.0362443263  0.00142215122 -0.0106232083
## mean_cpss      0.030714793  0.0282429323  0.00484169668 -0.0082476896
## mean_epsd      0.025424770 -0.0463684315  0.00946748435 -0.0019127169
## male           0.000630823  0.0063679527 -0.00262407430  0.0008361204
## gest_age_w    -0.035168407  0.0301476493 -0.00601412877 -0.0148466585
##                   obese_bmi concep_spring  concep_summer   concep_fall
## lat            0.0165669344  0.0143292896 -0.01403190526  0.0054905592
## lon            0.0097671301 -0.0004607517 -0.00711327850  0.0164218323
## lat_lon_int   -0.0098964732 -0.0120393632  0.00884440451  0.0018457750
## latina_re      0.0206541647 -0.0060643614 -0.00481142499  0.0173271022
## black_re       0.0069962872  0.0017220099 -0.00790581701 -0.0063828834
## other_re       0.0022620043  0.0044829491  0.00173196369 -0.0047479694
## ed_no_hs       0.0063181836 -0.0002364031 -0.00445308767  0.0110338032
## ed_hs          0.0244129738  0.0039578854 -0.00331835284  0.0022657370
## ed_aa          0.0094785197  0.0067611284 -0.01125776398 -0.0070846273
## ed_4yr        -0.0124024526 -0.0066354615  0.00647620043  0.0010078237
## low_bmi       -0.0066814978 -0.0050129897  0.00309812470  0.0032063724
## ovwt_bmi      -0.0523383998  0.0092806876 -0.00512123746  0.0026091436
## obese_bmi      0.1599105152 -0.0085938744 -0.00346392738  0.0005673674
## concep_spring -0.0085938744  0.1875696767 -0.06020066890 -0.0677257525
## concep_summer -0.0034639274 -0.0602006689  0.18302078356 -0.0653069756
## concep_fall    0.0005673674 -0.0677257525 -0.06530697563  0.1977350096
## concep_2010   -0.0043921206 -0.0236714146  0.00009331701  0.0287043120
## concep_2011    0.0032598742  0.0003633142 -0.00140348782 -0.0127396381
## concep_2012    0.0072737498 -0.0085677457  0.00186260750  0.0019559245
## concep_2013   -0.0059187868  0.0321545529 -0.00028368371 -0.0176182513
## maternal_age   0.0027900741 -0.0149065532  0.01490413862 -0.0196470231
## any_smoker     0.0027173913  0.0016983696  0.00024262422 -0.0023777174
## smokeSH        0.0110524666 -0.0041134138 -0.00627836837 -0.0028778966
## mean_cpss     -0.0087226114  0.0079650833  0.01166899615 -0.0055888831
## mean_epsd      0.0281330380 -0.0063209443 -0.01563660013  0.0265650931
## male          -0.0017804885 -0.0062746357 -0.00393797778  0.0018476768
## gest_age_w    -0.0214614301 -0.0179961830  0.01920131892  0.0141959621
##                  concep_2010   concep_2011  concep_2012   concep_2013
## lat            0.01106812411 -0.0220635440  0.002443596  0.0074817863
## lon            0.00844610317  0.0186983100 -0.007067638 -0.0206806648
## lat_lon_int   -0.00588610547  0.0255410960 -0.004770794 -0.0142344221
## latina_re     -0.00610790930 -0.0088215679  0.012520654  0.0015888776
## black_re       0.00904677297  0.0183859392 -0.014679388 -0.0125617136
## other_re      -0.00078013020 -0.0023739847  0.000455387  0.0027733815
## ed_no_hs      -0.00016299371  0.0096091635 -0.003536093 -0.0057396182
## ed_hs          0.00576574693 -0.0046335006  0.003715261 -0.0046409659
## ed_aa          0.00488483437  0.0024100673 -0.005564182 -0.0025879917
## ed_4yr         0.00035336041  0.0053402214 -0.006101688  0.0006519748
## low_bmi        0.00128404204  0.0043933648 -0.005352664 -0.0002874164
## ovwt_bmi      -0.00333452779  0.0055828456 -0.004354794  0.0023988692
## obese_bmi     -0.00439212056  0.0032598742  0.007273750 -0.0059187868
## concep_spring -0.02367141464  0.0003633142 -0.008567746  0.0321545529
## concep_summer  0.00009331701 -0.0014034878  0.001862608 -0.0002836837
## concep_fall    0.02870431199 -0.0127396381  0.001955925 -0.0176182513
## concep_2010    0.13567048893 -0.0488918916 -0.047448589 -0.0391495959
## concep_2011   -0.04889189162  0.2110780976 -0.088679776 -0.0731692447
## concep_2012   -0.04744858855 -0.0886797758  0.207464863 -0.0710092670
## concep_2013   -0.03914959588 -0.0731692447 -0.071009267  0.1835981048
## maternal_age  -0.02663971411 -0.0380704459  0.031448396  0.0348222009
## any_smoker     0.00266886646  0.0105298913 -0.011015140 -0.0020865683
## smokeSH        0.00631569517  0.0136280160 -0.018670867 -0.0021014990
## mean_cpss      0.00832724099 -0.0113573536 -0.011161856  0.0104924310
## mean_epsd     -0.01748485806  0.0347867417 -0.022850868  0.0069811381
## male           0.00089584329 -0.0029824116 -0.001761825  0.0044194935
## gest_age_w     0.01072301448 -0.0118973482 -0.026416733  0.0268056111
##               maternal_age    any_smoker      smokeSH    mean_cpss    mean_epsd
## lat            0.030778940 -0.0082274331 -0.011104226 -0.025836085 -0.034737548
## lon           -0.179809071  0.0227979933  0.046688554 -0.011147361  0.050844656
## lat_lon_int   -0.095594562  0.0156963705  0.027384613  0.017046231  0.048585549
## latina_re     -0.108588330 -0.0085888975 -0.005905100 -0.046683144  0.043223625
## black_re      -0.089596872  0.0185364907  0.034978948 -0.023312337  0.022057855
## other_re      -0.013307482 -0.0013586957  0.008424660  0.025560459  0.020267988
## ed_no_hs      -0.137612465  0.0179541925  0.030936455 -0.056115354  0.067010728
## ed_hs         -0.108683104  0.0017468944  0.024833522 -0.034338956  0.020146191
## ed_aa         -0.040296710  0.0110636646  0.022806677  0.030714793  0.025424770
## ed_4yr         0.109104452 -0.0156735248 -0.036244326  0.028242932 -0.046368432
## low_bmi       -0.010895294  0.0015527950  0.001422151  0.004841697  0.009467484
## ovwt_bmi       0.008900228 -0.0060656056 -0.010623208 -0.008247690 -0.001912717
## obese_bmi      0.002790074  0.0027173913  0.011052467 -0.008722611  0.028133038
## concep_spring -0.014906553  0.0016983696 -0.004113414  0.007965083 -0.006320944
## concep_summer  0.014904139  0.0002426242 -0.006278368  0.011668996 -0.015636600
## concep_fall   -0.019647023 -0.0023777174 -0.002877897 -0.005588883  0.026565093
## concep_2010   -0.026639714  0.0026688665  0.006315695  0.008327241 -0.017484858
## concep_2011   -0.038070446  0.0105298913  0.013628016 -0.011357354  0.034786742
## concep_2012    0.031448396 -0.0110151398 -0.018670867 -0.011161856 -0.022850868
## concep_2013    0.034822201 -0.0020865683 -0.002101499  0.010492431  0.006981138
## maternal_age   1.000000000 -0.0466296108 -0.155964054  0.100637638 -0.160410684
## any_smoker    -0.046629611  0.0794836957  0.049010093  0.017642908  0.042144665
## smokeSH       -0.155964054  0.0490100932  0.191419314  0.031721118  0.108180210
## mean_cpss      0.100637638  0.0176429080  0.031721118  1.000000000  0.455187203
## mean_epsd     -0.160410684  0.0421446647  0.108180210  0.455187203  1.000000000
## male           0.023413804  0.0023291925  0.002004449 -0.003315304  0.001541815
## gest_age_w     0.091663607 -0.0149814181 -0.050311537 -0.037142336 -0.137187808
##                         male   gest_age_w
## lat            0.02900476291  0.011119160
## lon           -0.02552947737 -0.039266472
## lat_lon_int   -0.03395191918 -0.024532454
## latina_re     -0.00087717989 -0.026393632
## black_re       0.00022022814 -0.036847127
## other_re       0.00033220855 -0.005475090
## ed_no_hs      -0.01350857023 -0.007692848
## ed_hs          0.00006345557 -0.017237679
## ed_aa          0.00063082298 -0.035168407
## ed_4yr         0.00636795270  0.030147649
## low_bmi       -0.00262407430 -0.006014129
## ovwt_bmi       0.00083612040 -0.014846658
## obese_bmi     -0.00178048853 -0.021461430
## concep_spring -0.00627463569 -0.017996183
## concep_summer -0.00393797778  0.019201319
## concep_fall    0.00184767678  0.014195962
## concep_2010    0.00089584329  0.010723014
## concep_2011   -0.00298241161 -0.011897348
## concep_2012   -0.00176182513 -0.026416733
## concep_2013    0.00441949355  0.026805611
## maternal_age   0.02341380415  0.091663607
## any_smoker     0.00232919255 -0.014981418
## smokeSH        0.00200444935 -0.050311537
## mean_cpss     -0.00331530432 -0.037142336
## mean_epsd      0.00154181454 -0.137187808
## male           0.25014184185 -0.007427180
## gest_age_w    -0.00742717951  1.000000000
ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.4 Response data: birth weight (in grams)

Y <- select(hs_data2, birth_weight) %>%
  as.matrix()
head(Y)
##      birth_weight
## [1,]         2860
## [2,]         2755
## [3,]         3505
## [4,]         2695
## [5,]         3355
## [6,]         3810

Distribution of birth weight and scaled birth weight

hist(Y, breaks = 20)

hist(scale(Y), breaks = 20)

1.5 Scatterplots of exposures and outcome (birth weight)

Both birth weight (Y) and the exposures are scaled here

NOTE: Don’t use these plots as a way to estimate how many predictors might make the cut. This should be done a priori

df <- as.data.frame(cbind(scale(Y), X.scaled))
# par(mfrow=c(5,4))
sapply(2:length(df), function(x){
  lm.x <- lm(birth_weight ~ df[,x], data = df)
  plot(df[,c(x, 1)],
       xlab = paste0(colnames(df)[x], " beta: ",
                     round(summary(lm.x)$coef[2,1],4),
                     "; p = ",
                     round(summary(lm.x)$coef[2,4],4)))
  abline(lm.x)
})

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2 Is gestational age a potenital mediator?

I.e., is there a relationship between our exposures and gestational age?

The DAG might look something like this:

exposures —> gestational age —> birth weight  _________________________________^

2.1 Scatter plots for exposures and gestational age

Both gestational age and the exposures are scaled here. Gestational age measured in weeks from estimated date of conception to delivery

Since there were some (small) relationships between exposures and gestational age (based on simple linear regression models– namely the ozone and SES indicators), I’m going to omit this covariate for now.

df2 <- as.data.frame(cbind(W.scaled[,"gest_age_w"], X.scaled))
colnames(df2)[1] <- "gest_age_w"
# par(mfrow=c(5,4))
sapply(2:length(df2), function(x){
  lm.x <- lm(gest_age_w ~ df2[,x], data = df2)
  plot(df2[,c(x, 1)],
       xlab = paste0(colnames(df2)[x], " beta: ",
                     round(summary(lm.x)$coef[2,1],4),
                     "; p = ",
                     round(summary(lm.x)$coef[2,4],4)))
  abline(lm.x)
})

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Dropping gest_age_w from the covariates

colnames(W.scaled)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"          "gest_age_w"
W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"

3 RIDGE regression

To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.

set.seed(123)

library(glmnet)
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## Loaded glmnet 4.0-2
lambda_seq <- 10^seq(4, -4, by = -.05)

#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
                      standardize = T, standardize.response = T)
plot(ridge_cv)

best_lambda <- ridge_cv$lambda.min
best_lambda
## [1] 891.2509
#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
                   standardize = T, standardize.response = T)
summary(bw_ridge)
##           Length Class     Mode   
## a0         1     -none-    numeric
## beta      21     dgCMatrix S4     
## df         1     -none-    numeric
## dim        2     -none-    numeric
## lambda     1     -none-    numeric
## dev.ratio  1     -none-    numeric
## nulldev    1     -none-    numeric
## npasses    1     -none-    numeric
## jerr       1     -none-    numeric
## offset     1     -none-    logical
## call       7     -none-    call   
## nobs       1     -none-    numeric

Ridge regression coefficients

coef(bw_ridge)
## 22 x 1 sparse Matrix of class "dgCMatrix"
##                                  s0
## (Intercept)         3756.2244127611
## mean_pm                6.5831658736
## mean_o3               -5.7909309972
## mean_temp             -2.6190406717
## pct_tree_cover         0.0346391254
## pct_impervious        -0.4281346032
## mean_aadt_intensity   -0.0002915500
## dist_m_tri            -0.0003520682
## dist_m_npl             0.0001168135
## dist_m_waste_site      0.0017447014
## dist_m_major_emit     -0.0003705192
## dist_m_cafo           -0.0003121004
## dist_m_mine_well      -0.0022906005
## cvd_rate_adj          -0.1469368176
## res_rate_adj          -0.1446242346
## violent_crime_rate    -0.4156388202
## property_crime_rate   -0.0143345439
## pct_less_hs           -0.6736508410
## pct_unemp             -3.6551596165
## pct_limited_eng       -0.5218862220
## pct_hh_pov            -0.4758794734
## pct_poc               -0.4466466437

Ridge regression predictions

ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)

actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))

The R2 value for this model is 0.03. Based on these results, it doesn’t look like there’s much here.

4 Nonparametric Bayesian Shrinkage (NPB): Birth weight

Still, we wanted to try to fit the NPB model with these data.

4.1 Finding the NPB priors

Start with Lauren’s from the example in the vignette

In an email from April 29, Lauren provided me with some additional guidance on finding the NPB priors:

  • Keep alpha.pi and beta.pi set to 1, and then let a.phi1 take values 1, 10, and 100 and see how the results change.
  • Keep a.phi1 set to 1 (or 10 or 100), and mess with alpha.pi and beta.pi.
    • Run the following code: alpha.pi=1 beta.pi=1 plot(density(rbeta(10000, alpha.pi, beta.pi))) and then change alpha.pi and beta.pi and see how it changes the prior distribution.
    • This is the distribution of the probability of a main effect regression coefficient being 0 (aka exclusion probability). We don’t want this to be too informative (you don’t want high mass around just a few values). Also alpha.pi and beta.pi don’t have to be the same value. You might try alpha.pi = 1 and beta.pi = 2 to get a slightly lower prior probability of exclusion. Try not to change all three (alpha.pi, beta.pi, and a.phi1) at once.
  • When playing with the priors, set “interact=FALSE” and just fit the modelwith the main effects. Most of the interactions were null anyway so it shouldn’t change the results too much and it will make the code run a lot faster. Then when you find a set of priors you like, you can add in “interact=TRUE” and “XWinteract=TRUE.”

Some additional feedback from Lauren during our 6/10 meeting:

  • The confidence intervals were really wide and heavily skewed. I’m going to try adjusting the sig2inv.mu1 parameter after the a.phi1 parameter to see if this helps
  • the rbeta distributions is interpreted as the exclusion probability, so I should try to aim to have most of the mass of that distribution in the middle, since we hypothesize that maybe 40-60% of the predictors will be important. The way to do this is to set alpha.pi and beta.pi to the same value
  • I should set the burn in number to be about half the iterations

Note: I’m including far fewer iterations of the priors than in the previous version of the document.

4.1.1 Vignette Priors

set.seed(123)

priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1)

fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects
##       Posterior Mean       SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    -0.06294726 1.687109    0.0000000            0 0.030
##  [2,]    -0.29091146 2.551404   -2.0623012            0 0.040
##  [3,]    -0.39619712 4.707586   -1.5182704            0 0.032
##  [4,]    -0.03913962 2.358689    0.0000000            0 0.018
##  [5,]    -0.24478491 1.883445    0.0000000            0 0.026
##  [6,]    -0.02992530 1.238033    0.0000000            0 0.018
##  [7,]    -0.06459764 1.187282    0.0000000            0 0.022
##  [8,]    -0.07195478 1.626867    0.0000000            0 0.026
##  [9,]     0.52187302 4.607456    0.0000000            0 0.022
## [10,]     0.15513912 2.716250    0.0000000            0 0.028
## [11,]    -0.26301331 3.031174   -0.4129585            0 0.030
## [12,]    -0.59623768 4.782450   -7.8170388            0 0.044
## [13,]    -0.41000284 3.325195   -2.0623012            0 0.034
## [14,]    -0.35348519 2.749343   -1.3278783            0 0.030
## [15,]    -0.05106869 2.246354    0.0000000            0 0.030
## [16,]    -0.05304155 1.567894    0.0000000            0 0.018
## [17,]    -0.08577037 1.819558    0.0000000            0 0.026
## [18,]    -1.15486876 6.567923  -16.6412947            0 0.054
## [19,]    -0.16285021 1.546441    0.0000000            0 0.026
## [20,]    -0.15357498 1.222171    0.0000000            0 0.026
## [21,]    -0.27218562 2.503071    0.0000000            0 0.022
plot(fit.npb.1$beta[,1], type = "l")

plot(fit.npb.1$beta[,2], type = "l")

plot(fit.npb.1$beta[,13], type = "l")

4.1.2 Adjust alpha.pi and beta.pi

For now, leave a.phi1 and sig2inv.mu1 alone for now.

alpha.pi and beta.pi are responsible for the exclusion probability distribution. If we think we want ~50% of our covariates, we need the mass of this distribution to be somewhere between 0.4 and 0.6. To do this, we set alpha.pi and beta.pi to the same value

4.1.2.1 Try making alpha.pi and beta.pi 2

plot(density(rbeta(10000, 2, 2)))

priors.npb.12 <- list(alpha.pi = 2, beta.pi = 2, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.12 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.12, interact = F)
npb.sum.12 <- summary(fit.npb.12)
npb.sum.12$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    -0.05585006  2.558733   -0.9107843    1.2488176 0.064
##  [2,]    -1.18895021  6.461003  -19.2446984    0.0000000 0.078
##  [3,]    -0.96419729  5.568817  -16.7861820    0.0000000 0.082
##  [4,]    -0.17391929  3.339516   -3.8588587    0.0000000 0.056
##  [5,]    -0.37209500  3.188349   -4.1881190    0.0000000 0.052
##  [6,]     0.01243140  2.401382   -1.1337072    0.0000000 0.052
##  [7,]    -0.05330369  2.623531   -0.8095384    0.0000000 0.050
##  [8,]     0.02179721  1.330539   -0.3965023    0.0000000 0.050
##  [9,]     1.04072127  7.198161    0.0000000   10.5356040 0.066
## [10,]     0.03250576  1.233531    0.0000000    0.0000000 0.046
## [11,]    -0.49881936  4.284310   -6.5704159    0.0000000 0.070
## [12,]    -1.13807809  6.103752  -19.1306487    0.0000000 0.094
## [13,]    -0.48738699  3.979972   -5.6423561    0.0000000 0.064
## [14,]    -0.52923656  4.432090   -7.3351997    0.0000000 0.068
## [15,]    -0.20711733  2.605385   -2.0372706    0.0000000 0.048
## [16,]    -0.23005353  2.320961   -2.0372706    0.0000000 0.056
## [17,]    -0.17426309  2.017873   -4.4027432    0.0000000 0.056
## [18,]    -2.81786531 10.058263  -42.6622076    0.0000000 0.122
## [19,]    -0.21014274  2.756962   -1.8169934    0.0000000 0.050
## [20,]    -0.22612120  1.957105   -2.0821434    0.0000000 0.050
## [21,]    -0.19384788  2.641713   -4.0618985    0.1994985 0.064
plot(fit.npb.12$beta[,1], type = "l")

plot(fit.npb.12$beta[,2], type = "l")

plot(fit.npb.12$beta[,13], type = "l")

4.1.2.2 Try making alpha.pi and beta.pi 5

plot(density(rbeta(10000, 5, 5)))

priors.npb.13 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.13 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.13, interact = F)
npb.sum.13 <- summary(fit.npb.13)
npb.sum.13$main.effects
##       Posterior Mean       SD 95% CI Lower 95% CI Upper   PIP
##  [1,]     -0.1739327 4.490772   -10.213958    9.9368147 0.188
##  [2,]     -1.4247428 8.176458   -16.181675    8.1882486 0.222
##  [3,]     -1.4403640 6.221568   -20.696307    4.3895425 0.216
##  [4,]     -0.3358477 4.528988    -9.591430    7.7615128 0.216
##  [5,]     -0.9969214 5.066390   -14.631366    3.8872951 0.202
##  [6,]     -0.1445406 3.433180    -8.468007    6.7668174 0.196
##  [7,]     -0.3991079 4.911675   -12.022636   10.2419437 0.216
##  [8,]      0.1189375 5.215748    -8.108638   11.3293838 0.184
##  [9,]      1.6358856 7.205395    -6.027428   25.5745080 0.232
## [10,]      0.3000110 3.435584    -5.658070   11.4664392 0.192
## [11,]     -1.3901896 8.247625   -20.467505    6.5096500 0.214
## [12,]     -1.4442944 6.338596   -20.938242    6.3300568 0.240
## [13,]     -1.3257189 6.613639   -19.727254    4.3277879 0.224
## [14,]     -1.3544745 5.246391   -16.688737    1.9619716 0.218
## [15,]      0.0139276 3.685508    -7.697730    5.4654433 0.172
## [16,]     -1.0157786 4.059599   -13.367519    1.8186189 0.182
## [17,]     -0.7172938 6.373838   -12.879427    4.3895425 0.202
## [18,]     -3.4726949 9.571950   -34.045190    2.1210054 0.294
## [19,]     -0.8775056 4.320639   -12.681860    3.3689995 0.196
## [20,]     -0.7384011 3.524475   -11.224363    0.7593049 0.164
## [21,]     -0.3347857 2.815050    -8.065163    3.0029989 0.166
plot(fit.npb.13$beta[,1], type = "l")

plot(fit.npb.13$beta[,2], type = "l")

plot(fit.npb.13$beta[,13], type = "l")

4.1.2.3 Try making alpha.pi and beta.pi 8

plot(density(rbeta(10000, 8, 8)))

priors.npb.14 <- list(alpha.pi = 8, beta.pi = 8, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.14 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.14, interact = F)
npb.sum.14 <- summary(fit.npb.14)
npb.sum.14$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]     -0.7542073  4.727682   -13.375772     9.369699 0.304
##  [2,]     -3.0212801  9.232142   -30.064091     5.032394 0.362
##  [3,]     -1.2184191  6.055311   -16.912434     8.907677 0.300
##  [4,]     -0.8547605  5.402424   -14.998936     8.390509 0.288
##  [5,]     -1.3986793  5.953325   -17.081301     4.853341 0.276
##  [6,]     -0.5251034  4.559356   -12.719423     9.369699 0.262
##  [7,]     -0.7089094  5.409248   -13.043111     9.241721 0.294
##  [8,]      0.1735833  6.132190    -9.558869    14.202827 0.290
##  [9,]      1.4331513  8.023282    -8.366645    23.124217 0.280
## [10,]     -0.2391486  4.648372   -11.790578     9.571535 0.278
## [11,]     -1.8979572  7.780447   -22.351703     8.666068 0.336
## [12,]     -2.1739360  7.330178   -25.275595     8.758575 0.388
## [13,]     -1.7110317  6.148423   -17.052794     4.839192 0.294
## [14,]     -1.8875976  5.800864   -15.372856     3.905622 0.304
## [15,]     -0.4933873  3.705164   -10.128855     5.771647 0.224
## [16,]     -1.4644885  5.293402   -16.840640     4.853341 0.290
## [17,]     -1.5884687  4.980539   -16.912434     4.806950 0.314
## [18,]     -5.3458715 12.474886   -47.674022     3.972676 0.418
## [19,]     -1.0264207  5.150193   -15.429091     7.863305 0.296
## [20,]     -0.9030834  4.267366   -12.228600     6.677137 0.272
## [21,]     -0.8473787  4.576029   -12.281218     6.497990 0.274
plot(fit.npb.14$beta[,1], type = "l")

plot(fit.npb.14$beta[,2], type = "l")

plot(fit.npb.14$beta[,13], type = "l")

4.1.3 Set alpha.pi and beta.pi to 5, readjust a.phi1 and sig2inv.mu1

Set alpha.pi and beta.pi to 5, rather than 8, and try adjusting a.phi1 and sig2inv.mu1

4.1.3.1 Try making a.phi1 = 10 and sig2inv.mu1 = 1

priors.npb.23 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 1)

fit.npb.23 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.23, interact = F)
npb.sum.23 <- summary(fit.npb.23)
npb.sum.23$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]     -0.5873083  4.918398   -12.342901     8.711006 0.246
##  [2,]     -3.8048904 13.456931   -39.722335     5.668791 0.332
##  [3,]     -1.6873544  7.578959   -16.168928     5.668321 0.300
##  [4,]     -0.3056229  4.523096   -10.595951     7.953071 0.244
##  [5,]     -1.2289691  5.306702   -14.074921     5.736699 0.280
##  [6,]     -0.1743268  4.616332   -10.091337     9.432144 0.252
##  [7,]     -0.3454703  5.704442   -11.607307    16.708223 0.260
##  [8,]     -0.1315553  5.063896    -9.860011    10.799674 0.232
##  [9,]      2.4614174  9.930215    -7.405537    37.951814 0.308
## [10,]      0.2377121  4.839663    -9.722982    11.712248 0.230
## [11,]     -4.1208739 21.528436   -52.278068    11.932845 0.352
## [12,]     -2.3069329  8.236088   -24.465618     6.055165 0.326
## [13,]     -1.3318387  5.953807   -16.819478     7.907002 0.278
## [14,]     -1.7582919  6.385090   -18.183169     5.668791 0.284
## [15,]     -0.5116488  4.584157    -9.937609     5.839274 0.240
## [16,]     -1.4645731  5.161296   -15.815723     5.525176 0.294
## [17,]     -1.2366149  6.005428   -18.133263     5.870796 0.260
## [18,]     -5.2824150 13.446943   -49.920837     3.103663 0.366
## [19,]     -0.6781444  4.791220   -12.897476     7.609749 0.258
## [20,]     -0.6484217  5.260639   -13.456143     8.180968 0.248
## [21,]     -0.6545086  4.834557   -11.437506     6.286956 0.222
plot(fit.npb.23$beta[,1], type = "l")

plot(fit.npb.23$beta[,2], type = "l")

plot(fit.npb.23$beta[,13], type = "l")

4.1.3.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10

priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 10)

fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]     -0.2602480  6.321456   -13.744945    13.838969 0.260
##  [2,]     -2.9383247 10.328329   -36.545051     7.628224 0.316
##  [3,]     -1.3957413  7.009138   -20.979797     9.520137 0.290
##  [4,]     -0.2305071  5.067001   -12.707187    10.119051 0.250
##  [5,]     -1.2506499  6.225976   -18.573920     6.773117 0.250
##  [6,]     -0.1414881  4.242075    -9.397693     8.396127 0.226
##  [7,]     -0.4909395  5.925732   -12.959531    10.107668 0.244
##  [8,]      0.2986060  5.456119   -10.368056    13.646438 0.262
##  [9,]      3.7845724 12.155981    -5.949447    51.084993 0.312
## [10,]      0.7249301  6.134249    -8.188400    16.691562 0.258
## [11,]     -1.0511460 15.923305   -24.977724    23.721207 0.344
## [12,]     -1.8498651  7.316253   -24.546506     7.505480 0.272
## [13,]     -0.9879859  5.686595   -15.871228     5.777184 0.254
## [14,]     -2.1277142  7.975941   -23.293444     5.168810 0.274
## [15,]     -0.4265771  4.214481   -10.174425     7.653653 0.218
## [16,]     -1.1747947  5.568738   -18.464146     9.101806 0.286
## [17,]     -1.4413812  5.728937   -18.138404     4.856576 0.276
## [18,]     -6.2212032 14.097082   -53.785694     2.011623 0.364
## [19,]     -0.5736030  4.600584   -12.862286     8.285742 0.242
## [20,]     -0.7877488  5.438677   -14.547267     9.016658 0.230
## [21,]     -0.2710370  5.503657   -12.348355     9.848989 0.238
plot(fit.npb.24$beta[,1], type = "l")

plot(fit.npb.24$beta[,2], type = "l")

plot(fit.npb.24$beta[,13], type = "l")

4.2 Fit the NPB model without temperature

Below I’ve used the set of priors labeled “24” and set scaleY = T

The priors are as follows: r priors.npb.24

Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.

priors.npb <- priors.npb.24

#' Exposures (minus temperature)
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(3)], Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Birth_Weight_v4.1.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4.1.rdata"))
npb.sum <- summary(fit.npb)

4.2.1 First, main effect regression coefficients with PIPs

rownames(npb.sum$main.effects) <- colnames(X.scaled[,-c(3)])
npb.sum$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                -0.39311629  5.948287   -13.793001   10.7646248 0.1812
## mean_o3              -133.45924031 95.282493  -280.870320    1.4166975 0.8032
## pct_tree_cover          0.12721285  5.311107   -10.223723   12.6643926 0.1780
## pct_impervious         -0.70088765  5.123154   -14.188222    6.4138402 0.1800
## mean_aadt_intensity     0.35475982  5.230087    -8.714796   13.2645464 0.1668
## dist_m_tri             -0.18341960  5.428993   -12.867837   11.6968190 0.1776
## dist_m_npl              0.55391982  5.969792    -8.463951   16.7125172 0.1728
## dist_m_waste_site       3.43354109 11.364150    -4.896414   42.6424558 0.2272
## dist_m_major_emit       0.67721995  5.837771    -8.351270   16.6815966 0.1696
## dist_m_cafo            -1.63593647 18.422799   -40.210811   22.7887508 0.2388
## dist_m_mine_well       -1.71586374  7.465745   -24.795214    7.3103901 0.2196
## cvd_rate_adj           -0.95469604  6.845516   -18.333719    6.3757417 0.1948
## res_rate_adj           -2.00711286  8.311984   -25.072347    3.7978670 0.2128
## violent_crime_rate     -0.01728102  4.902578   -10.898684   12.6340426 0.1644
## property_crime_rate    -1.07099605  5.323785   -16.716705    4.8809724 0.1820
## pct_less_hs            -0.69940998  6.130446   -16.760072    9.3378765 0.2052
## pct_unemp              -7.40692974 16.622892   -58.385635    0.7882151 0.3300
## pct_limited_eng        -0.52770287  5.713158   -13.794315    8.9179180 0.1820
## pct_hh_pov             -0.59773462  6.363955   -16.122840    8.7457755 0.1772
## pct_poc                 0.30759474  6.638556   -10.919232   15.5608535 0.1772

4.2.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum$interactions
##          Posterior Mean           SD 95% CI Lower 95% CI Upper    PIP
##   [1,]   0.077512245499   1.89496902       0.0000       0.0000 0.0036
##   [2,]  -0.005298254770   0.16183541       0.0000       0.0000 0.0016
##   [3,]  -0.001160855197   0.10434367       0.0000       0.0000 0.0016
##   [4,]   0.018777573001   0.80899803       0.0000       0.0000 0.0020
##   [5,]  -0.008397274677   0.22122332       0.0000       0.0000 0.0028
##   [6,]  -0.009954516915   0.33661058       0.0000       0.0000 0.0028
##   [7,]  -0.017486523183   0.48198359       0.0000       0.0000 0.0024
##   [8,]  -0.022295212401   0.62083315       0.0000       0.0000 0.0040
##   [9,]  -0.038337018229   0.87255923       0.0000       0.0000 0.0064
##  [10,]  -0.022562657529   0.56250101       0.0000       0.0000 0.0060
##  [11,]  -0.006885025261   0.19264045       0.0000       0.0000 0.0016
##  [12,]  -0.017422756289   0.57495746       0.0000       0.0000 0.0024
##  [13,]  -0.008001421013   0.27600655       0.0000       0.0000 0.0032
##  [14,]  -0.021756743249   0.41111900       0.0000       0.0000 0.0060
##  [15,]  -0.015524688102   0.53380824       0.0000       0.0000 0.0012
##  [16,]  -0.018793646043   0.49327965       0.0000       0.0000 0.0036
##  [17,]  -0.018369868490   0.40306195       0.0000       0.0000 0.0032
##  [18,]  -0.006740261188   0.23711426       0.0000       0.0000 0.0020
##  [19,]  -0.019959681945   0.56628631       0.0000       0.0000 0.0028
##  [20,]  -0.043354340685   1.03737057       0.0000       0.0000 0.0052
##  [21,]  -0.015333683037   0.39445346       0.0000       0.0000 0.0040
##  [22,]  -0.019971193952   0.54992357       0.0000       0.0000 0.0028
##  [23,]  -0.095180540938   1.97478195       0.0000       0.0000 0.0056
##  [24,]  -0.036270396704   0.85726619       0.0000       0.0000 0.0048
##  [25,]  -0.038615863869   0.91345921       0.0000       0.0000 0.0064
##  [26,]  -0.006761029442   0.55120606       0.0000       0.0000 0.0032
##  [27,]  -0.036809623474   0.84759368       0.0000       0.0000 0.0052
##  [28,]  -0.025083023398   0.80142309       0.0000       0.0000 0.0040
##  [29,]   0.007553754461   0.22185302       0.0000       0.0000 0.0028
##  [30,]  -0.001200522442   0.06643487       0.0000       0.0000 0.0012
##  [31,]   0.000176397720   0.51778312       0.0000       0.0000 0.0020
##  [32,]  -0.008181183832   0.31138968       0.0000       0.0000 0.0040
##  [33,]   0.010033332885   0.65362821       0.0000       0.0000 0.0028
##  [34,]  -0.009695057530   0.21646088       0.0000       0.0000 0.0036
##  [35,]   0.005076217196   0.48059341       0.0000       0.0000 0.0016
##  [36,]   0.059769235885   1.41738566       0.0000       0.0000 0.0044
##  [37,]   0.017421036520   0.81440692       0.0000       0.0000 0.0020
##  [38,]  -0.008407800031   0.22382709       0.0000       0.0000 0.0020
##  [39,]  -0.002694557126   0.11360342       0.0000       0.0000 0.0028
##  [40,]  -0.003395487393   0.13981938       0.0000       0.0000 0.0016
##  [41,]  -0.013577252339   0.33129376       0.0000       0.0000 0.0040
##  [42,]  -0.007046543852   0.15362712       0.0000       0.0000 0.0044
##  [43,]  -0.000123786182   0.10077732       0.0000       0.0000 0.0020
##  [44,]  -0.004328980807   0.13926453       0.0000       0.0000 0.0020
##  [45,]  -0.012789846170   0.34334581       0.0000       0.0000 0.0032
##  [46,]  -0.024663312481   0.51887645       0.0000       0.0000 0.0036
##  [47,]  -0.007203608045   0.19428973       0.0000       0.0000 0.0020
##  [48,]  -0.032378503667   0.73030831       0.0000       0.0000 0.0032
##  [49,]  -0.010237491116   0.30843818       0.0000       0.0000 0.0024
##  [50,]  -0.002033904596   0.06490260       0.0000       0.0000 0.0012
##  [51,]  -0.009621355509   0.23595696       0.0000       0.0000 0.0032
##  [52,]  -0.000685817864   0.15901782       0.0000       0.0000 0.0028
##  [53,]  -0.010945578269   0.30924523       0.0000       0.0000 0.0024
##  [54,]  -0.000004910094   0.08906645       0.0000       0.0000 0.0012
##  [55,]  -0.002212792862   0.08182682       0.0000       0.0000 0.0008
##  [56,]  -0.000982894147   0.14175300       0.0000       0.0000 0.0016
##  [57,]  -0.000288530570   0.16239534       0.0000       0.0000 0.0020
##  [58,]   0.000095084952   0.45587023       0.0000       0.0000 0.0032
##  [59,]   0.002678497175   0.15597690       0.0000       0.0000 0.0016
##  [60,]  -0.008182310718   0.37790417       0.0000       0.0000 0.0012
##  [61,]  -0.009307878739   0.30044668       0.0000       0.0000 0.0024
##  [62,]  -0.019665894256   0.80483252       0.0000       0.0000 0.0020
##  [63,]  -0.016684208717   0.33889285       0.0000       0.0000 0.0036
##  [64,]  -0.000680385092   0.29343203       0.0000       0.0000 0.0032
##  [65,]  -0.004621935099   0.18110914       0.0000       0.0000 0.0012
##  [66,]  -0.008793210097   0.23891642       0.0000       0.0000 0.0032
##  [67,]  -0.002142233879   0.08042036       0.0000       0.0000 0.0020
##  [68,]  -0.000380506438   0.07000530       0.0000       0.0000 0.0012
##  [69,]  -0.001896693125   0.30146905       0.0000       0.0000 0.0032
##  [70,]  -0.007851682195   0.17330574       0.0000       0.0000 0.0028
##  [71,]  -0.010239781940   0.45879213       0.0000       0.0000 0.0028
##  [72,]  -0.010690713674   0.27299207       0.0000       0.0000 0.0016
##  [73,]   0.002638809087   0.17331978       0.0000       0.0000 0.0016
##  [74,]   0.006083910248   0.46686724       0.0000       0.0000 0.0024
##  [75,]  -0.029498169537   0.74049370       0.0000       0.0000 0.0036
##  [76,]  -0.025498977739   0.63017252       0.0000       0.0000 0.0052
##  [77,]  -0.019301178931   0.50799476       0.0000       0.0000 0.0024
##  [78,]  -0.032412711778   0.68447550       0.0000       0.0000 0.0048
##  [79,]  -0.028799308739   0.94104293       0.0000       0.0000 0.0040
##  [80,]  -0.013384160916   0.43589164       0.0000       0.0000 0.0016
##  [81,]  -0.005484627207   0.20036842       0.0000       0.0000 0.0032
##  [82,]  -0.007494145400   0.18952267       0.0000       0.0000 0.0036
##  [83,]  -0.003613591771   0.15415321       0.0000       0.0000 0.0020
##  [84,]  -0.005053699309   0.14112229       0.0000       0.0000 0.0020
##  [85,]  -0.006982414069   0.14577281       0.0000       0.0000 0.0028
##  [86,]  -0.004937437350   0.14708010       0.0000       0.0000 0.0024
##  [87,]  -0.007812918939   0.20685045       0.0000       0.0000 0.0028
##  [88,]  -0.004849593313   0.13753056       0.0000       0.0000 0.0036
##  [89,]  -0.004059936450   0.15447152       0.0000       0.0000 0.0032
##  [90,]  -0.017677382019   0.65414722       0.0000       0.0000 0.0028
##  [91,]  -0.006124942207   0.15031641       0.0000       0.0000 0.0024
##  [92,]  -0.002483117215   0.13722482       0.0000       0.0000 0.0020
##  [93,]  -0.000966677298   0.26925429       0.0000       0.0000 0.0028
##  [94,]  -0.012099985261   0.24864205       0.0000       0.0000 0.0052
##  [95,]  -0.003204285707   0.13485572       0.0000       0.0000 0.0028
##  [96,]  -0.004395285951   0.19623737       0.0000       0.0000 0.0012
##  [97,]  -0.015028436815   0.89264435       0.0000       0.0000 0.0028
##  [98,]  -0.007027746465   0.28352978       0.0000       0.0000 0.0036
##  [99,]  -0.004805866368   0.28027578       0.0000       0.0000 0.0040
## [100,]  -0.002038783488   0.51285203       0.0000       0.0000 0.0048
## [101,]   0.001871846950   0.22228945       0.0000       0.0000 0.0024
## [102,]  -0.005608339642   0.52452090       0.0000       0.0000 0.0032
## [103,]  -0.004601605301   0.18074209       0.0000       0.0000 0.0020
## [104,]  -0.005290265834   0.13517970       0.0000       0.0000 0.0024
## [105,]   0.001041263000   0.05416414       0.0000       0.0000 0.0016
## [106,]  -0.009408797966   0.29870742       0.0000       0.0000 0.0020
## [107,]  -0.004368345305   0.11586400       0.0000       0.0000 0.0024
## [108,]  -0.018079400628   0.38696222       0.0000       0.0000 0.0056
## [109,]  -0.010739364747   0.24278489       0.0000       0.0000 0.0028
## [110,]  -0.000899320561   0.15484962       0.0000       0.0000 0.0016
## [111,]  -0.002733989559   0.15934891       0.0000       0.0000 0.0008
## [112,]  -0.006901598987   0.21183052       0.0000       0.0000 0.0012
## [113,]  -0.013122656849   0.28468625       0.0000       0.0000 0.0032
## [114,]  -0.001225235548   0.05325179       0.0000       0.0000 0.0016
## [115,]  -0.005017143823   0.15984198       0.0000       0.0000 0.0020
## [116,]  -0.013687087028   0.44939705       0.0000       0.0000 0.0032
## [117,]  -0.013401826431   0.37390840       0.0000       0.0000 0.0028
## [118,]  -0.008311581675   0.26876849       0.0000       0.0000 0.0024
## [119,]  -0.004979924718   0.12583790       0.0000       0.0000 0.0028
## [120,]  -0.030695805814   0.88456000       0.0000       0.0000 0.0032
## [121,]  -0.003010495154   0.15630415       0.0000       0.0000 0.0024
## [122,]   0.004678198800   0.45911338       0.0000       0.0000 0.0036
## [123,]  -0.001514044161   0.23809974       0.0000       0.0000 0.0032
## [124,]  -0.002629925505   0.22684441       0.0000       0.0000 0.0020
## [125,]   0.018508022256   0.71701990       0.0000       0.0000 0.0028
## [126,]   0.032326217611   1.01166937       0.0000       0.0000 0.0032
## [127,]  -0.007262420412   0.27284106       0.0000       0.0000 0.0040
## [128,]  -0.008986799405   0.26190968       0.0000       0.0000 0.0040
## [129,]   0.000830477174   0.17285671       0.0000       0.0000 0.0024
## [130,]  -0.007739926066   0.17038214       0.0000       0.0000 0.0036
## [131,]  -0.006403244079   0.17791750       0.0000       0.0000 0.0028
## [132,]  -0.049322649312   0.97354164       0.0000       0.0000 0.0052
## [133,]  -0.006199439995   0.15131092       0.0000       0.0000 0.0028
## [134,]  -0.007433494998   0.23429242       0.0000       0.0000 0.0020
## [135,]  -0.011626964697   0.31876094       0.0000       0.0000 0.0024
## [136,]  -0.087717839466   1.34801416       0.0000       0.0000 0.0072
## [137,]  -0.009896477695   0.58712701       0.0000       0.0000 0.0036
## [138,]  -0.005845459873   0.55751215       0.0000       0.0000 0.0020
## [139,]  -0.003893880626   0.09254771       0.0000       0.0000 0.0024
## [140,]  -0.009331434446   0.20597057       0.0000       0.0000 0.0040
## [141,]  -0.005290820506   0.18534477       0.0000       0.0000 0.0024
## [142,]  -0.014160704367   0.46057932       0.0000       0.0000 0.0040
## [143,]   0.006548270830   0.84439280       0.0000       0.0000 0.0044
## [144,]  -0.016534454016   0.63114076       0.0000       0.0000 0.0036
## [145,]  -0.000743731879   0.18726986       0.0000       0.0000 0.0032
## [146,]   0.005629224616   0.87487921       0.0000       0.0000 0.0036
## [147,]  -0.001885812761   0.06666402       0.0000       0.0000 0.0008
## [148,]  -0.006853640653   0.28890763       0.0000       0.0000 0.0020
## [149,]  -0.016886973654   0.57879872       0.0000       0.0000 0.0052
## [150,]   0.088176025928   2.49946228       0.0000       0.0000 0.0044
## [151,]  -0.005032309945   0.44359419       0.0000       0.0000 0.0044
## [152,]   0.460360915559   6.09240456       0.0000       0.0000 0.0072
## [153,]   0.009904258508   0.44693117       0.0000       0.0000 0.0012
## [154,]   0.006369996039   0.64866633       0.0000       0.0000 0.0036
## [155,]  -0.018168072642   0.54272884       0.0000       0.0000 0.0020
## [156,]  -0.006950947588   0.25517209       0.0000       0.0000 0.0036
## [157,]  -0.028441997020   0.77396040       0.0000       0.0000 0.0052
## [158,]  -0.031438190004   0.91907014       0.0000       0.0000 0.0032
## [159,]  -0.035949666595   0.73064300       0.0000       0.0000 0.0044
## [160,]  -0.055600250410   1.42848689       0.0000       0.0000 0.0044
## [161,]  -0.023424757390   0.92293117       0.0000       0.0000 0.0028
## [162,]  -0.008355301606   0.41118450       0.0000       0.0000 0.0024
## [163,]  -0.008702671421   0.23509290       0.0000       0.0000 0.0020
## [164,]  -0.018930217339   0.57088414       0.0000       0.0000 0.0020
## [165,]  -0.007054164651   0.17089812       0.0000       0.0000 0.0036
## [166,]  -0.011531392593   0.24583542       0.0000       0.0000 0.0036
## [167,]  -0.013920935909   0.47660180       0.0000       0.0000 0.0024
## [168,]  -0.021687352799   0.53107472       0.0000       0.0000 0.0032
## [169,]  -0.006235543396   0.26695442       0.0000       0.0000 0.0036
## [170,]  -0.001786552499   0.07251393       0.0000       0.0000 0.0016
## [171,]   0.003195470475   0.28006495       0.0000       0.0000 0.0024
## [172,]  -0.004427810396   0.10873510       0.0000       0.0000 0.0020
## [173,]  -0.009374655990   0.38268627       0.0000       0.0000 0.0020
## [174,]  -0.003939932469   0.16060707       0.0000       0.0000 0.0012
## [175,]  -0.007789877717   0.17415907       0.0000       0.0000 0.0036
## [176,]  -0.012744445781   0.38174079       0.0000       0.0000 0.0028
## [177,]   0.004466348868   0.31293835       0.0000       0.0000 0.0020
## [178,]  -0.007832020733   0.20889112       0.0000       0.0000 0.0016
## [179,]  -0.013316978907   0.42171627       0.0000       0.0000 0.0032
## [180,]  -0.007378904438   0.20904764       0.0000       0.0000 0.0016
## [181,]  -0.002363686577   0.07080393       0.0000       0.0000 0.0012
## [182,]  -0.002109121434   0.10545607       0.0000       0.0000 0.0004
## [183,]  -0.008373893622   0.44144683       0.0000       0.0000 0.0032
## [184,]  -0.005349413410   0.15876989       0.0000       0.0000 0.0032
## [185,]  -0.010421388360   0.22119655       0.0000       0.0000 0.0044
## [186,]  -0.002358323393   0.17696427       0.0000       0.0000 0.0024
## [187,]  -0.015370081806   0.53638266       0.0000       0.0000 0.0032
## [188,]  -0.006910410996   0.22141540       0.0000       0.0000 0.0032
## [189,]  -0.022299813209   0.55500876       0.0000       0.0000 0.0044
## [190,]   0.001432083286   0.16194854       0.0000       0.0000 0.0032
## [191,]  -0.012634815637   0.37150946       0.0000       0.0000 0.0024
## [192,]  -0.002476931496   0.72110086       0.0000       0.0000 0.0044
## [193,]  -0.011541440828   0.37092716       0.0000       0.0000 0.0048
## [194,]  -0.001812540242   0.07299083       0.0000       0.0000 0.0012
## [195,]  -0.022650101138   0.63309011       0.0000       0.0000 0.0028
## [196,]  -0.017124308379   0.39028057       0.0000       0.0000 0.0036
## [197,]  -0.007016610432   0.17868011       0.0000       0.0000 0.0020
## [198,]  -0.027951602254   0.59965340       0.0000       0.0000 0.0028
## [199,]  -0.032157006751   0.84031165       0.0000       0.0000 0.0052
## [200,]   0.001770217780   0.18249179       0.0000       0.0000 0.0028
## [201,]  -0.002607830949   0.60632484       0.0000       0.0000 0.0044
## [202,]  -0.117962535313   3.16720430       0.0000       0.0000 0.0044
## [203,]   0.015890031859   1.11338722       0.0000       0.0000 0.0016
## [204,]  -0.011393190217   0.23832728       0.0000       0.0000 0.0036
## [205,]  -0.005952055238   0.54722136       0.0000       0.0000 0.0040
## [206,]  -0.038880581002   1.69054443       0.0000       0.0000 0.0032
## [207,]  -0.060309080347   1.50936835       0.0000       0.0000 0.0044
## [208,]  -0.008408289794   0.30173105       0.0000       0.0000 0.0024
## [209,]  -0.016708747035   0.43501863       0.0000       0.0000 0.0048
## [210,]  -0.036996132081   1.60376743       0.0000       0.0000 0.0036
## [211,]  -0.010025915962   0.28318353       0.0000       0.0000 0.0032
## [212,]  -0.012908625589   0.67700740       0.0000       0.0000 0.0020
## [213,]  -0.005632161730   0.37899967       0.0000       0.0000 0.0040
## [214,]   0.005602421145   0.40715103       0.0000       0.0000 0.0028
## [215,]  -0.006195531724   0.23486162       0.0000       0.0000 0.0040
## [216,]   0.002443425311   0.14271602       0.0000       0.0000 0.0012
## [217,]   0.051492801765   1.71514530       0.0000       0.0000 0.0020
## [218,]  -0.001820967610   0.18761642       0.0000       0.0000 0.0028
## [219,]  -0.051019931124   1.06937379       0.0000       0.0000 0.0068
## [220,]  -0.017584732265   0.79461153       0.0000       0.0000 0.0012
## [221,]  -0.017956496917   0.95172341       0.0000       0.0000 0.0048
## [222,]   0.035111481585   1.82633618       0.0000       0.0000 0.0040
## [223,]  -0.015422612226   0.44979819       0.0000       0.0000 0.0040
## [224,]  -0.028728253838   0.70493964       0.0000       0.0000 0.0036
## [225,]  -0.044613299504   1.60773822       0.0000       0.0000 0.0040
## [226,]  -0.017417108250   0.41623596       0.0000       0.0000 0.0028
## [227,]   0.180534172821   7.12024754       0.0000       0.0000 0.0036
## [228,]  -0.006219468135   0.19058906       0.0000       0.0000 0.0028
## [229,]  -0.016641311239   0.51874280       0.0000       0.0000 0.0036
## [230,] -33.907272204583  80.99992459    -263.5669       0.0000 0.1612
## [231,] 125.316644805642 165.76860874       0.0000     421.2932 0.3788
## [232,] 224.384231193351 150.66154945       0.0000     429.2850 0.7220
## [233,]  -0.007129334558   0.18365299       0.0000       0.0000 0.0020
## [234,]  -0.114389087966   3.16981639       0.0000       0.0000 0.0048
## [235,]   0.020634365000   1.56782220       0.0000       0.0000 0.0032
## [236,]   0.011706957504   0.54813246       0.0000       0.0000 0.0028
## [237,]  -0.001754630321   0.09789813       0.0000       0.0000 0.0012
## [238,]  -0.071574448465   1.95184403       0.0000       0.0000 0.0072
## [239,]  -0.016239302590   0.49002803       0.0000       0.0000 0.0048
## [240,]  -0.002913153664   0.20938889       0.0000       0.0000 0.0036
## [241,]  -0.005092926960   0.14393816       0.0000       0.0000 0.0020
## [242,]  -0.007776978452   0.31419267       0.0000       0.0000 0.0024
## [243,]  -0.001020290328   0.54226916       0.0000       0.0000 0.0068
## [244,]  -0.021114116590   0.50988963       0.0000       0.0000 0.0056
## [245,]  -0.043481702815   1.29522567       0.0000       0.0000 0.0040
## [246,]   0.010684798469   1.22658287       0.0000       0.0000 0.0036
## [247,]  -0.010988989664   0.39088790       0.0000       0.0000 0.0028
## [248,]  -0.006456506044   0.29951611       0.0000       0.0000 0.0020
## [249,]   0.104288829300   3.13911634       0.0000       0.0000 0.0040
## [250,]  -0.005318214276   0.14514869       0.0000       0.0000 0.0020
## [251,]   0.040656227177   1.67361747       0.0000       0.0000 0.0048
## [252,]   0.008342514625   0.50499930       0.0000       0.0000 0.0024
## [253,]  -0.166198912126   5.72215479       0.0000       0.0000 0.0044
## [254,]  -0.002408477666   0.17538300       0.0000       0.0000 0.0032
## [255,]  -0.015021949283   0.44086480       0.0000       0.0000 0.0044
## [256,]  -0.012980660987   0.35505351       0.0000       0.0000 0.0032
## [257,]  -0.013041055889   0.32730973       0.0000       0.0000 0.0028
## [258,]  -0.002335719680   0.22882591       0.0000       0.0000 0.0020
## [259,]  -0.008911431793   0.30276611       0.0000       0.0000 0.0020
## [260,]   0.022901204205   1.38929822       0.0000       0.0000 0.0028
## [261,]  -0.014421660615   0.29955962       0.0000       0.0000 0.0032
## [262,]  -0.008570716687   0.36679942       0.0000       0.0000 0.0032
## [263,]  -0.003180901842   0.26902081       0.0000       0.0000 0.0020
## [264,]  -0.007991874354   0.30415555       0.0000       0.0000 0.0028
## [265,]   0.015038041340   0.89455184       0.0000       0.0000 0.0020
## [266,]   0.005647313259   0.48810658       0.0000       0.0000 0.0032
## [267,]  -0.004995964291   0.23868191       0.0000       0.0000 0.0028
## [268,]  -0.006166713796   0.34439277       0.0000       0.0000 0.0032
## [269,]  -0.016879645471   0.48189746       0.0000       0.0000 0.0032
## [270,]  -0.014815231216   0.33178299       0.0000       0.0000 0.0052
## [271,]  -0.009982153750   0.18233922       0.0000       0.0000 0.0048
## [272,]  -0.011340553854   0.63603377       0.0000       0.0000 0.0036
## [273,]  -0.023923887643   0.78848404       0.0000       0.0000 0.0028
## [274,]   0.006458824121   0.74375192       0.0000       0.0000 0.0032
## [275,]   0.037680454896   2.01371049       0.0000       0.0000 0.0040
## [276,]   0.002479658689   0.09028084       0.0000       0.0000 0.0016
## [277,]  -0.011312725415   0.35494331       0.0000       0.0000 0.0032
## [278,]  -0.043162506508   1.19810998       0.0000       0.0000 0.0040
## [279,]  -0.006838457712   0.32067735       0.0000       0.0000 0.0036
## [280,]  -0.019213023376   0.57667296       0.0000       0.0000 0.0044
## [281,]  -0.012212189128   0.27715059       0.0000       0.0000 0.0028
## [282,]  -0.026361413932   0.75561607       0.0000       0.0000 0.0036
## [283,]  -0.026834747068   0.75182482       0.0000       0.0000 0.0028
## [284,]  -0.003255720210   0.32825826       0.0000       0.0000 0.0028
## [285,]  -0.009367942869   0.32182682       0.0000       0.0000 0.0012
## [286,]  -0.033143251151   0.99083277       0.0000       0.0000 0.0024
## [287,]  -0.011803803834   0.80870457       0.0000       0.0000 0.0040
## [288,]   0.007377977298   0.86117365       0.0000       0.0000 0.0036
## [289,]  -0.020202892637   0.74130391       0.0000       0.0000 0.0028
## [290,]  -0.005021878853   0.21603853       0.0000       0.0000 0.0028
## [291,]  -0.001373631684   0.09094959       0.0000       0.0000 0.0024
## [292,]  -0.048804733320   0.88417673       0.0000       0.0000 0.0052
## [293,]  -0.005239325387   0.31315263       0.0000       0.0000 0.0028
## [294,]  -0.005761661118   0.14565685       0.0000       0.0000 0.0020
## [295,]  -0.002696221424   0.24430534       0.0000       0.0000 0.0020
## [296,]  -0.008944684671   0.25642179       0.0000       0.0000 0.0016
## [297,]  -0.032102557686   0.73032886       0.0000       0.0000 0.0028
## [298,]   0.017014141302   1.17841481       0.0000       0.0000 0.0028
## [299,]  -0.004471695110   0.17336421       0.0000       0.0000 0.0020
## [300,]   0.018079525846   1.23574077       0.0000       0.0000 0.0036
## [301,]   0.195433190885   4.41676573       0.0000       0.0000 0.0044
## [302,]  -0.055320559885   1.29695642       0.0000       0.0000 0.0056
## [303,]  -0.019572748917   0.73533091       0.0000       0.0000 0.0016
## [304,]  -0.011212201799   0.28471926       0.0000       0.0000 0.0028
## [305,]   0.009655037266   0.50448854       0.0000       0.0000 0.0036
## [306,]  -0.051756361217   1.20456760       0.0000       0.0000 0.0032
## [307,]   0.023146107980   1.97622196       0.0000       0.0000 0.0036
## [308,]  -0.020261138479   0.48772513       0.0000       0.0000 0.0044
## [309,]  -0.006048449287   0.36604985       0.0000       0.0000 0.0028
## [310,]  -0.003036588924   0.51232017       0.0000       0.0000 0.0032
## [311,]  -0.023760443550   0.75120128       0.0000       0.0000 0.0024
## [312,]   0.000513771491   0.16222306       0.0000       0.0000 0.0016
## [313,]  -0.004691392345   0.14701344       0.0000       0.0000 0.0028
## [314,]   0.019242669204   1.22957977       0.0000       0.0000 0.0032
## [315,]  -0.063155044407   1.16172232       0.0000       0.0000 0.0060
## [316,]   0.003960064312   0.49890612       0.0000       0.0000 0.0024
## [317,]  -0.018387291383   0.45892809       0.0000       0.0000 0.0044
## [318,]  -0.025321026779   0.54712480       0.0000       0.0000 0.0036
## [319,]  -0.009172373987   0.36574748       0.0000       0.0000 0.0020
## [320,]   0.004471295764   0.68004294       0.0000       0.0000 0.0024
## [321,]  -0.006222273541   0.16120961       0.0000       0.0000 0.0032
## [322,]  -0.005351276394   0.16486304       0.0000       0.0000 0.0012
## [323,]  -0.000756712110   0.23307087       0.0000       0.0000 0.0032
## [324,]   0.035118506232   1.11793869       0.0000       0.0000 0.0044
## [325,]  -0.070072871925   2.41384578       0.0000       0.0000 0.0044
## [326,]  -0.022851360251   0.55227440       0.0000       0.0000 0.0044
## [327,]   0.303114071056   7.50652176       0.0000       0.0000 0.0044
## [328,]  -0.011582931448   0.36700925       0.0000       0.0000 0.0044
## [329,]  -0.010613303991   0.30852646       0.0000       0.0000 0.0036
## [330,]  -0.027075429771   0.71533992       0.0000       0.0000 0.0040
## [331,]  -0.136515534391   5.00352438       0.0000       0.0000 0.0064
## [332,]  -0.022852912267   0.75756922       0.0000       0.0000 0.0016
## [333,]   0.020187965065   1.27962210       0.0000       0.0000 0.0020
## [334,]  -0.011198888118   0.29089284       0.0000       0.0000 0.0028
## [335,]  -0.029612202899   0.87041331       0.0000       0.0000 0.0024
## [336,]   0.011261559803   0.85853034       0.0000       0.0000 0.0024
## [337,]  -0.020022792972   0.47069933       0.0000       0.0000 0.0048
## [338,]   0.024969097024   1.17305983       0.0000       0.0000 0.0020
## [339,]  -0.027600721038   0.82426743       0.0000       0.0000 0.0040
## [340,]   0.013676085979   1.48261263       0.0000       0.0000 0.0032
## [341,]  -0.009960766137   0.38510385       0.0000       0.0000 0.0028
## [342,]  -0.004626082776   0.15514131       0.0000       0.0000 0.0016
## [343,]  -0.058113023425   1.99160512       0.0000       0.0000 0.0048
## [344,]  -0.003576015220   0.13273758       0.0000       0.0000 0.0020
## [345,]  -0.027536745453   0.50736955       0.0000       0.0000 0.0052
## [346,]   0.000838694644   0.16778729       0.0000       0.0000 0.0028
## [347,]  -0.011085183933   0.26265430       0.0000       0.0000 0.0036
## [348,]  -0.005107677264   0.25301642       0.0000       0.0000 0.0032
## [349,]  -0.004856572184   0.29701811       0.0000       0.0000 0.0024
## [350,]   0.004556981535   0.34060245       0.0000       0.0000 0.0020
## [351,]   0.002686377947   0.84127635       0.0000       0.0000 0.0048
## [352,]   0.112032013353   3.88625998       0.0000       0.0000 0.0028
## [353,]   0.000620992412   0.17669093       0.0000       0.0000 0.0016
## [354,]  -0.007932905494   0.23962659       0.0000       0.0000 0.0036
## [355,]  -0.007698990492   0.30625395       0.0000       0.0000 0.0012
## [356,]  -0.012379647947   0.39697120       0.0000       0.0000 0.0024
## [357,]  -0.133481285946   3.71427129       0.0000       0.0000 0.0028
## [358,]  -0.013633108636   0.48070025       0.0000       0.0000 0.0036
## [359,]  -0.004775638365   0.24799706       0.0000       0.0000 0.0024
## [360,]  -0.014865099772   0.26392615       0.0000       0.0000 0.0044
## [361,]  -0.013028027990   0.47305657       0.0000       0.0000 0.0028
## [362,]  -0.005468360752   0.56241295       0.0000       0.0000 0.0032
## [363,]   0.002664616226   0.49170200       0.0000       0.0000 0.0024
## [364,]  -0.009012269528   0.31874325       0.0000       0.0000 0.0044
## [365,]  -0.025250216200   0.51819062       0.0000       0.0000 0.0036
## [366,]   0.033990586807   1.36422364       0.0000       0.0000 0.0048
## [367,]  -0.011564044832   0.22974409       0.0000       0.0000 0.0040
## [368,]  -0.005287871768   1.16521946       0.0000       0.0000 0.0052
## [369,]  -0.046373672971   1.72550110       0.0000       0.0000 0.0032
## [370,]  -0.001327961004   0.04988299       0.0000       0.0000 0.0008
## [371,]  -0.003350765615   0.09001085       0.0000       0.0000 0.0020
## [372,]  -0.013706814901   0.48731227       0.0000       0.0000 0.0040
## [373,]  -0.009985312451   0.55920415       0.0000       0.0000 0.0024
## [374,]  -0.002061742848   0.28214207       0.0000       0.0000 0.0024
## [375,]  -0.001634246021   0.24366186       0.0000       0.0000 0.0032
## [376,]  -0.012074633919   0.36456348       0.0000       0.0000 0.0036
## [377,]  -0.010834068024   0.35549701       0.0000       0.0000 0.0020
## [378,]   0.086027185070   3.31533568       0.0000       0.0000 0.0028
## [379,]  -0.015261375287   0.58226749       0.0000       0.0000 0.0024
## [380,]   0.023021678997   1.44169857       0.0000       0.0000 0.0032
## [381,]   0.011825022435   0.62472885       0.0000       0.0000 0.0016
## [382,]   0.038187616486   2.39971102       0.0000       0.0000 0.0024
## [383,]  -0.016067021985   0.29576709       0.0000       0.0000 0.0040
## [384,]   0.043028531193   1.35079836       0.0000       0.0000 0.0032
## [385,]   0.000953473230   0.23238143       0.0000       0.0000 0.0024
## [386,]   0.034483566455   1.29241912       0.0000       0.0000 0.0032
## [387,]   0.003572152871   0.14463305       0.0000       0.0000 0.0012
## [388,]  -0.002769892940   0.10768519       0.0000       0.0000 0.0024
## [389,]  -0.013725305103   0.46288595       0.0000       0.0000 0.0032
## [390,]   0.006872941892   1.11014968       0.0000       0.0000 0.0032
## [391,]  -0.044645332545   1.16879028       0.0000       0.0000 0.0032
## [392,]  -0.012516194905   0.35498164       0.0000       0.0000 0.0032
## [393,]  -0.011854270025   0.38168649       0.0000       0.0000 0.0024
## [394,]   0.025735469350   1.69073070       0.0000       0.0000 0.0036
## [395,]  -0.014199661505   0.29394990       0.0000       0.0000 0.0032
## [396,]   0.000119278353   0.50802763       0.0000       0.0000 0.0028
## [397,]  -0.012533581499   0.37626573       0.0000       0.0000 0.0032
## [398,]   0.036482953408   1.23835802       0.0000       0.0000 0.0020
## [399,]  -0.021064055475   0.55056925       0.0000       0.0000 0.0040
## [400,]  -0.008589237883   0.25959581       0.0000       0.0000 0.0036
## [401,]  -0.000855132109   0.06048833       0.0000       0.0000 0.0016
## [402,]  -0.010484993058   0.36046966       0.0000       0.0000 0.0036
## [403,]   0.026571658208   0.91360492       0.0000       0.0000 0.0024
## [404,]   0.082552285007   2.77598208       0.0000       0.0000 0.0020
## [405,]   0.006287517269   0.46502031       0.0000       0.0000 0.0036
## [406,]  -0.016016487443   0.50079087       0.0000       0.0000 0.0016
## [407,]  -0.000892802764   0.04464014       0.0000       0.0000 0.0004
## [408,]  -0.012604446775   0.57469000       0.0000       0.0000 0.0024
## [409,]   0.396263790114  10.26549594       0.0000       0.0000 0.0056
## [410,]   0.019869451314   0.91001043       0.0000       0.0000 0.0036
## [411,]  -0.001707686372   0.21671028       0.0000       0.0000 0.0020
## [412,]  -0.011214084365   0.33155186       0.0000       0.0000 0.0032
## [413,]   0.046124367420   2.39444469       0.0000       0.0000 0.0032
## [414,]  -0.009949361209   0.26015842       0.0000       0.0000 0.0036
## [415,]  -0.006214543507   0.17406293       0.0000       0.0000 0.0020
## [416,]  -0.008197063067   0.20960794       0.0000       0.0000 0.0020
## [417,]  -0.004128841164   0.24439932       0.0000       0.0000 0.0024
## [418,]   0.008908130946   0.42391829       0.0000       0.0000 0.0016
## [419,]  -0.004790055314   0.16211120       0.0000       0.0000 0.0020
## [420,]  -0.006996292163   0.40181681       0.0000       0.0000 0.0020
## [421,]  -0.005943375332   0.29256176       0.0000       0.0000 0.0032
## [422,]  -0.011219922691   0.24633748       0.0000       0.0000 0.0032
## [423,]  -0.013359934322   0.46105063       0.0000       0.0000 0.0032
## [424,]  -0.009646134834   0.35545901       0.0000       0.0000 0.0044
## [425,]  -0.010267933686   0.28406853       0.0000       0.0000 0.0040
## [426,]   0.004928885200   0.28363202       0.0000       0.0000 0.0024
## [427,]  -0.007913616611   0.20394257       0.0000       0.0000 0.0032
## [428,]  -0.009971763039   0.35111822       0.0000       0.0000 0.0020
## [429,]  -0.023026589938   0.46129726       0.0000       0.0000 0.0064
## [430,]  -0.047661401918   2.87190435       0.0000       0.0000 0.0020
## [431,]   0.010315006588   1.36643922       0.0000       0.0000 0.0028
## [432,]  -0.064872677911   2.00078262       0.0000       0.0000 0.0044
## [433,]  -0.026481186038   0.66641742       0.0000       0.0000 0.0040
## [434,]  -0.000004613592   0.53591395       0.0000       0.0000 0.0028
## [435,]  -0.189017401660   6.32076040       0.0000       0.0000 0.0048
## [436,]  -0.015416631897   0.49268606       0.0000       0.0000 0.0028
## [437,]  -0.005914756284   0.20951584       0.0000       0.0000 0.0036
## [438,]  -0.035202532604   1.31435145       0.0000       0.0000 0.0056
## [439,]   0.000864842619   0.16967549       0.0000       0.0000 0.0012
## [440,]   0.024882275225   1.42758835       0.0000       0.0000 0.0020
## [441,]   0.002916338979   1.29871986       0.0000       0.0000 0.0032
## [442,]   0.255644481711   5.51174596       0.0000       0.0000 0.0048
## [443,]  -0.176581075195   3.85591371       0.0000       0.0000 0.0052
## [444,]  -0.003223499988   0.09362844       0.0000       0.0000 0.0012
## [445,]  -0.003291208277   0.08620111       0.0000       0.0000 0.0016
## [446,]   0.045279758559   2.29388131       0.0000       0.0000 0.0012
## [447,]  -0.145103429871   4.11086429       0.0000       0.0000 0.0032
## [448,]  -0.005045429543   0.22276876       0.0000       0.0000 0.0036
## [449,]  -0.007219412531   0.32637856       0.0000       0.0000 0.0028
## [450,]  -0.042414047639   1.13263838       0.0000       0.0000 0.0040
## [451,]  -0.006752753096   0.29425845       0.0000       0.0000 0.0016
## [452,]  -0.006642052272   0.20632750       0.0000       0.0000 0.0028
## [453,]  -0.003260015099   0.21958897       0.0000       0.0000 0.0028
## [454,]  -0.019764476720   1.51870367       0.0000       0.0000 0.0040
## [455,]  -0.014635162741   0.33117654       0.0000       0.0000 0.0040
## [456,]  -0.017524400237   0.48981384       0.0000       0.0000 0.0028
## [457,]   0.000613960557   1.76763564       0.0000       0.0000 0.0056
## [458,]  -0.032506873177   0.72701478       0.0000       0.0000 0.0044
## [459,]   0.004492014672   0.99674425       0.0000       0.0000 0.0028
## [460,]  -0.010857580374   0.22946604       0.0000       0.0000 0.0032
## [461,]  -0.083928584962   3.35899159       0.0000       0.0000 0.0036
## [462,]  -0.003210033329   0.51652083       0.0000       0.0000 0.0036
## [463,]  -0.005412946931   0.59008516       0.0000       0.0000 0.0036
## [464,]   0.056655425709   2.11745607       0.0000       0.0000 0.0040
## [465,]  -0.001757576277   0.11864214       0.0000       0.0000 0.0012
## [466,]   0.030095838087   1.50915027       0.0000       0.0000 0.0020
## [467,]  -0.001035491660   0.14161547       0.0000       0.0000 0.0020
## [468,]   0.157153047450   4.08484444       0.0000       0.0000 0.0056
## [469,]  -0.501167138980   6.94176613       0.0000       0.0000 0.0084
## [470,]  -0.005864811932   0.14345439       0.0000       0.0000 0.0024
## [471,]  -0.007521824822   0.28119883       0.0000       0.0000 0.0012
## [472,]  -0.017664332554   0.38227394       0.0000       0.0000 0.0036
## [473,]  -0.022794198273   0.75056323       0.0000       0.0000 0.0040
## [474,]  -0.008122664465   0.23457787       0.0000       0.0000 0.0032
## [475,]  -0.000570720243   0.14677310       0.0000       0.0000 0.0024
## [476,]  -0.055271195076   1.15912258       0.0000       0.0000 0.0040
## [477,]  -0.018209359069   0.46598573       0.0000       0.0000 0.0040
## [478,]  -0.008989387522   0.20621976       0.0000       0.0000 0.0028
## [479,]  -0.022098228392   0.59556353       0.0000       0.0000 0.0032
## [480,]  -0.014798313755   0.34237484       0.0000       0.0000 0.0036
## [481,]  -0.030811412279   0.78359251       0.0000       0.0000 0.0040
## [482,]  -0.010462487169   0.36372320       0.0000       0.0000 0.0032
## [483,]  -0.009553250795   0.21859034       0.0000       0.0000 0.0028
## [484,]  -0.035094755904   0.66957076       0.0000       0.0000 0.0060
## [485,]  -0.014185713509   0.75026832       0.0000       0.0000 0.0012
## [486,]  -0.069400797529   1.56749596       0.0000       0.0000 0.0044
## [487,]   0.022225816636   1.44211026       0.0000       0.0000 0.0024
## [488,]  -0.000814332077   0.05881846       0.0000       0.0000 0.0016
## [489,]   0.030652800466   2.01602913       0.0000       0.0000 0.0024
## [490,]  -0.063511586442   1.83717117       0.0000       0.0000 0.0052
## [491,]  -0.022700435253   0.65233127       0.0000       0.0000 0.0036
## [492,]  -0.098988597375   1.83086640       0.0000       0.0000 0.0064
## [493,]  -0.061138117183   1.44615929       0.0000       0.0000 0.0040
## [494,]  -0.028977269874   0.56791369       0.0000       0.0000 0.0052
## [495,]   0.179461170017   4.30722934       0.0000       0.0000 0.0056
## [496,]  -0.020746580736   0.49649779       0.0000       0.0000 0.0040
## [497,]  -0.001249536694   0.05333634       0.0000       0.0000 0.0008
## [498,]  -0.016785978894   0.38648805       0.0000       0.0000 0.0044
## [499,]  -0.019295338254   0.73393324       0.0000       0.0000 0.0032
## [500,]  -0.001705272436   0.08106644       0.0000       0.0000 0.0020
## [501,]  -0.009320098823   0.34428257       0.0000       0.0000 0.0048
## [502,]  -0.020579309741   0.60320725       0.0000       0.0000 0.0028
## [503,]  -0.010579131130   0.27413676       0.0000       0.0000 0.0036
## [504,]  -0.015625402209   0.38461180       0.0000       0.0000 0.0028
## [505,]  -0.003465160983   0.44691444       0.0000       0.0000 0.0036
## [506,]  -0.034178257023   1.32446694       0.0000       0.0000 0.0036
## [507,]  -0.003282160136   0.11718758       0.0000       0.0000 0.0024
## [508,]  -0.079900639171   3.70909207       0.0000       0.0000 0.0020
## [509,]  -0.022431191211   0.81056200       0.0000       0.0000 0.0044
## [510,]  -0.022556904613   0.55338928       0.0000       0.0000 0.0036
## [511,]  -0.004804816504   0.62932993       0.0000       0.0000 0.0028
## [512,]  -0.059047498651   1.71730101       0.0000       0.0000 0.0048
## [513,]  -0.049384745245   1.83429442       0.0000       0.0000 0.0036
## [514,]   0.005494034545   0.56134232       0.0000       0.0000 0.0020
## [515,]  -0.006508956080   0.65905558       0.0000       0.0000 0.0052
## [516,]  -0.004285743677   0.13191288       0.0000       0.0000 0.0016
## [517,]  -0.018760834483   0.47392307       0.0000       0.0000 0.0048
## [518,]  -0.013060060266   0.28714344       0.0000       0.0000 0.0040
## [519,]  -0.088945088286   2.67713887       0.0000       0.0000 0.0040
## [520,]  -0.033183602478   1.10743811       0.0000       0.0000 0.0044
## [521,]   0.022961557115   2.49921459       0.0000       0.0000 0.0044
## [522,]  -0.002753312513   0.60169682       0.0000       0.0000 0.0036
## [523,]   0.009940005950   0.47406672       0.0000       0.0000 0.0028
## [524,]  -0.013746396463   0.80165107       0.0000       0.0000 0.0016
## [525,]  -0.003150786565   0.09874495       0.0000       0.0000 0.0016
## [526,]  -0.007611354024   0.20498903       0.0000       0.0000 0.0024
## [527,]  -0.003380114448   0.23543710       0.0000       0.0000 0.0020
## [528,]  -0.003807895245   0.12689367       0.0000       0.0000 0.0016
## [529,]  -0.007760740077   0.16803559       0.0000       0.0000 0.0032
## [530,]  -0.017343753181   0.49024380       0.0000       0.0000 0.0020
## [531,]  -0.014023991678   0.37174580       0.0000       0.0000 0.0036
## [532,]   0.052562334358   2.43610598       0.0000       0.0000 0.0044
## [533,]  -0.000283980116   0.87552374       0.0000       0.0000 0.0048
## [534,]   0.464749466494  11.91636870       0.0000       0.0000 0.0028
## [535,]  -0.074286737829   3.16923526       0.0000       0.0000 0.0024
## [536,]  -0.007876414016   0.33482475       0.0000       0.0000 0.0028
## [537,]   0.021782869377   2.05632223       0.0000       0.0000 0.0052
## [538,]  -0.007914592358   0.33057970       0.0000       0.0000 0.0024
## [539,]  -0.774356709426  13.67150222       0.0000       0.0000 0.0096
## [540,]  -0.011778566516   0.59453434       0.0000       0.0000 0.0036
## [541,]  -0.003276766029   0.60973817       0.0000       0.0000 0.0016
## [542,]   0.000221146883   0.12136305       0.0000       0.0000 0.0020
## [543,]  -0.014927210584   0.38546086       0.0000       0.0000 0.0024
## [544,]   0.001732601875   0.10543250       0.0000       0.0000 0.0020
## [545,]  -0.005355088445   0.31086625       0.0000       0.0000 0.0032
## [546,]  -0.020654317960   0.81575844       0.0000       0.0000 0.0024
## [547,]   0.014406902980   0.77668193       0.0000       0.0000 0.0012
## [548,]  -0.004317814990   0.13330173       0.0000       0.0000 0.0016
## [549,]   0.002656498440   0.63489761       0.0000       0.0000 0.0028
## [550,]  -0.080657558973   4.02170030       0.0000       0.0000 0.0028
## [551,]  -0.002816920976   0.10063180       0.0000       0.0000 0.0028
## [552,]  -0.034095244342   0.87157644       0.0000       0.0000 0.0048
## [553,]  -0.010288863370   0.21383924       0.0000       0.0000 0.0036
## [554,]  -0.016936772088   0.34921923       0.0000       0.0000 0.0032
## [555,]  -0.016916878721   0.44830582       0.0000       0.0000 0.0036
## [556,]  -0.002131643117   0.23677563       0.0000       0.0000 0.0020
## [557,]  -0.008034583189   0.22000369       0.0000       0.0000 0.0032
## [558,]   0.003474978408   0.53153364       0.0000       0.0000 0.0028
## [559,]  -0.073074770882   3.39393812       0.0000       0.0000 0.0028
## [560,]   0.995346323365  18.98664737       0.0000       0.0000 0.0068
## [561,]  -0.008361229634   0.69708772       0.0000       0.0000 0.0032
## [562,]  -0.008900678750   0.28099606       0.0000       0.0000 0.0036
## [563,]  -0.003169279209   0.18225499       0.0000       0.0000 0.0020
## [564,]  -0.007455046290   0.45430185       0.0000       0.0000 0.0024
## [565,]  -0.553607251307  12.44386865       0.0000       0.0000 0.0044
## [566,]  -0.031097529903   0.95242426       0.0000       0.0000 0.0028
## [567,]   0.033929332045   1.84680767       0.0000       0.0000 0.0024
## [568,]   0.006420916800   0.69561144       0.0000       0.0000 0.0032
## [569,]  -0.001318280345   0.06330835       0.0000       0.0000 0.0012
## [570,]  -0.003786120176   0.10416923       0.0000       0.0000 0.0036
## [571,]  -0.067514826452   1.82259256       0.0000       0.0000 0.0052
## [572,]  -0.018480958496   0.59704822       0.0000       0.0000 0.0044
## [573,]  -0.002993372278   0.87881149       0.0000       0.0000 0.0020
## [574,]  -0.026665993702   0.67894368       0.0000       0.0000 0.0036
## [575,]  -0.013776910474   0.41310765       0.0000       0.0000 0.0036
## [576,]  -0.001973292930   0.17470236       0.0000       0.0000 0.0036
## [577,]  -0.004438100219   0.11678357       0.0000       0.0000 0.0016
## [578,]  -0.014336832509   0.42599314       0.0000       0.0000 0.0040
## [579,]  -0.010695960857   0.41082516       0.0000       0.0000 0.0028
## [580,]  -0.011240614581   0.53315641       0.0000       0.0000 0.0036
## [581,]   0.024615250029   1.42011973       0.0000       0.0000 0.0032
## [582,]  -0.022181753995   0.59309048       0.0000       0.0000 0.0024
## [583,]  -0.013463444964   0.38264027       0.0000       0.0000 0.0024
## [584,]   0.008152163610   0.55528023       0.0000       0.0000 0.0032
## [585,]  -0.017991033221   0.64669970       0.0000       0.0000 0.0064
## [586,]   0.014118159874   1.14160560       0.0000       0.0000 0.0028
## [587,]   0.011893440774   1.80420078       0.0000       0.0000 0.0040
## [588,]  -0.011175240984   0.44230741       0.0000       0.0000 0.0044
## [589,]  -0.002967471426   0.10849327       0.0000       0.0000 0.0024
## [590,]  -0.019706237996   0.74245661       0.0000       0.0000 0.0036
## [591,]  -0.004649083400   0.25496328       0.0000       0.0000 0.0040
## [592,]   0.045989309754   1.54812278       0.0000       0.0000 0.0028
## [593,]  -0.024345876969   0.62356136       0.0000       0.0000 0.0032
## [594,]  -0.032672501055   0.82374121       0.0000       0.0000 0.0032
## [595,]  -0.020045275100   0.45435262       0.0000       0.0000 0.0036
## [596,]  -0.017751756048   0.42098731       0.0000       0.0000 0.0028
## [597,]  -0.004200200904   0.12712235       0.0000       0.0000 0.0028
## [598,]  -0.032053802515   0.79772780       0.0000       0.0000 0.0036
## [599,]   0.016842502887   1.15927199       0.0000       0.0000 0.0036
## [600,]  -0.070318349761   2.34183355       0.0000       0.0000 0.0036
## [601,]  -0.009934425937   0.22625343       0.0000       0.0000 0.0028
## [602,]  -0.003822300287   0.25921719       0.0000       0.0000 0.0032
## [603,]   0.078653606168   3.22467748       0.0000       0.0000 0.0052
## [604,]  -0.008605321340   0.20144946       0.0000       0.0000 0.0028
## [605,]  -0.004510164259   0.14325420       0.0000       0.0000 0.0016
## [606,]  -0.034148517363   1.38981093       0.0000       0.0000 0.0032
## [607,]  -0.004578201489   0.15501365       0.0000       0.0000 0.0012
## [608,]  -0.046768490188   1.05353002       0.0000       0.0000 0.0048
## [609,]  -0.009612838960   0.25317189       0.0000       0.0000 0.0020
## [610,]  -0.009443713908   0.30636062       0.0000       0.0000 0.0040
## [611,]  -0.031408458855   0.75666644       0.0000       0.0000 0.0036
## [612,]   0.012237555232   0.70421566       0.0000       0.0000 0.0016
## [613,]  -0.041370550266   1.41840911       0.0000       0.0000 0.0040
## [614,]   0.016212102270   1.44872369       0.0000       0.0000 0.0048
## [615,]  -0.013145600858   0.29685104       0.0000       0.0000 0.0036
## [616,]  -0.169625771841   3.55407620       0.0000       0.0000 0.0048
## [617,]  -0.039240453614   1.88188869       0.0000       0.0000 0.0012
## [618,]  -0.005269214571   0.13439005       0.0000       0.0000 0.0020
## [619,]  -0.003076526626   0.11242850       0.0000       0.0000 0.0008
## [620,]  -0.057347446895   1.72495953       0.0000       0.0000 0.0040
## [621,]  -0.011371596143   0.98735479       0.0000       0.0000 0.0048
## [622,]  -0.250565496010   5.10554648       0.0000       0.0000 0.0048
## [623,]  -0.009690965036   0.27072685       0.0000       0.0000 0.0024
## [624,]  -0.057029533979   1.43915305       0.0000       0.0000 0.0056
## [625,]  -0.007817776412   0.28733881       0.0000       0.0000 0.0048
## [626,]  -0.007797170403   0.31795585       0.0000       0.0000 0.0024
## [627,]  -0.006623926491   0.15153783       0.0000       0.0000 0.0032
## [628,]  -0.100584447923   3.30292160       0.0000       0.0000 0.0032
## [629,]  -0.000750548337   1.86389532       0.0000       0.0000 0.0024
## [630,]  -0.009994159569   0.28833917       0.0000       0.0000 0.0024
## [631,]  -0.008820477452   0.29645074       0.0000       0.0000 0.0028
## [632,]  -0.135969615972   2.92828590       0.0000       0.0000 0.0052
## [633,]  -0.046100760987   1.31614838       0.0000       0.0000 0.0040
## [634,]  -0.030565850949   0.86583021       0.0000       0.0000 0.0036
## [635,]  -0.004687051834   0.16612548       0.0000       0.0000 0.0012
## [636,]  -0.014218244861   0.29578696       0.0000       0.0000 0.0044
## [637,]  -0.024397549719   0.69739803       0.0000       0.0000 0.0028
## [638,]  -0.009109701633   0.30240794       0.0000       0.0000 0.0032
## [639,]  -0.015944040292   0.45663594       0.0000       0.0000 0.0040
## [640,]   0.005106850522   0.44492338       0.0000       0.0000 0.0032
## [641,]  -0.034725268937   1.05783585       0.0000       0.0000 0.0036
## [642,]  -0.002950209840   0.09647124       0.0000       0.0000 0.0016
## [643,]  -0.006754035141   0.23679572       0.0000       0.0000 0.0032
## [644,]  -0.005597849972   0.45902215       0.0000       0.0000 0.0028
## [645,]  -0.008401471546   0.21035583       0.0000       0.0000 0.0024
## [646,]  -0.074121482245   2.40581668       0.0000       0.0000 0.0048
## [647,]  -0.000425346588   0.02126733       0.0000       0.0000 0.0004
## [648,]   0.000790630084   1.23113757       0.0000       0.0000 0.0052
## [649,]   0.000432618888   0.45784420       0.0000       0.0000 0.0028
## [650,]  -0.145741880389   3.06906657       0.0000       0.0000 0.0060
## [651,]  -0.003172104505   0.15537365       0.0000       0.0000 0.0024
## [652,]  -0.046685507757   2.12214954       0.0000       0.0000 0.0020
## [653,]  -0.006322497032   0.44991788       0.0000       0.0000 0.0028
## [654,]  -0.009285743890   0.37759836       0.0000       0.0000 0.0016
## [655,]  -0.019928334809   0.45214208       0.0000       0.0000 0.0052
## [656,]  -0.008927225596   0.30104603       0.0000       0.0000 0.0028
## [657,]  -0.007741397982   0.39154993       0.0000       0.0000 0.0028
## [658,]   0.001901749969   0.49295936       0.0000       0.0000 0.0032
## [659,]  -0.000902512254   0.46114259       0.0000       0.0000 0.0024
## [660,]  -0.023507615978   0.78984557       0.0000       0.0000 0.0020
## [661,]  -0.013813288202   0.28322338       0.0000       0.0000 0.0040
## [662,]  -0.013262506029   0.89450226       0.0000       0.0000 0.0028
## [663,]  -0.007781624225   0.34611303       0.0000       0.0000 0.0028
## [664,]  -0.010712713851   0.30412599       0.0000       0.0000 0.0028
## [665,]  -0.020013209795   0.48264855       0.0000       0.0000 0.0044
## [666,]  -0.020541068779   0.67968047       0.0000       0.0000 0.0028
## [667,]  -0.002081986442   0.66398277       0.0000       0.0000 0.0032
## [668,]  -0.001262570350   0.19777942       0.0000       0.0000 0.0036
## [669,]  -0.125840149299   4.35283419       0.0000       0.0000 0.0036
## [670,]  -0.031285405701   0.80892019       0.0000       0.0000 0.0040
## [671,]  -0.007278798419   0.16380178       0.0000       0.0000 0.0028
## [672,]  -0.010209893880   0.23977147       0.0000       0.0000 0.0040
## [673,]   0.009811294667   1.27920515       0.0000       0.0000 0.0040
## [674,]  -0.007947498264   0.34641686       0.0000       0.0000 0.0028
## [675,]  -0.005791236191   0.29189248       0.0000       0.0000 0.0020
## [676,]  -0.053490016820   1.63004683       0.0000       0.0000 0.0040
## [677,]   0.194583478820   4.10970132       0.0000       0.0000 0.0056
## [678,]  -0.043785140039   1.74606556       0.0000       0.0000 0.0028
## [679,]  -0.003447889209   0.14727196       0.0000       0.0000 0.0032
## [680,]  -0.008915141107   0.22148593       0.0000       0.0000 0.0020
## [681,]   0.017033912052   0.90012528       0.0000       0.0000 0.0044
## [682,]  -0.017604969427   0.78929270       0.0000       0.0000 0.0040
## [683,]  -0.027235175958   0.66938179       0.0000       0.0000 0.0044
## [684,]  -0.032355980424   1.12553618       0.0000       0.0000 0.0028
## [685,]  -0.017507957697   0.37029523       0.0000       0.0000 0.0032
## [686,]  -0.048300964822   0.89400333       0.0000       0.0000 0.0052
## [687,]  -0.011742198467   0.31410257       0.0000       0.0000 0.0032
## [688,]  -0.015020094874   0.52608758       0.0000       0.0000 0.0032
## [689,]  -0.018215787255   0.73945197       0.0000       0.0000 0.0016
## [690,]  -0.009254200946   0.26726327       0.0000       0.0000 0.0020
## [691,]   0.005392508159   0.62818751       0.0000       0.0000 0.0040
## [692,]   0.038890417125   1.94198815       0.0000       0.0000 0.0028
## [693,]  -0.008626612042   0.30274520       0.0000       0.0000 0.0032
## [694,]  -0.015015194116   0.36140886       0.0000       0.0000 0.0056
## [695,]   0.000175715370   0.67762016       0.0000       0.0000 0.0024
## [696,]   0.030391267528   1.92721371       0.0000       0.0000 0.0032
## [697,]  -0.007146066126   0.28393743       0.0000       0.0000 0.0036
## [698,]  -0.018913558711   0.47086016       0.0000       0.0000 0.0028
## [699,]  -0.009935667563   0.49938961       0.0000       0.0000 0.0036
## [700,]  -0.009733700596   0.38928790       0.0000       0.0000 0.0044
## [701,]  -0.021805086197   0.67868523       0.0000       0.0000 0.0036
## [702,]  -0.377516491970   6.38360871       0.0000       0.0000 0.0068
## [703,]   0.609401326224   8.00923605       0.0000       0.0000 0.0088
## [704,]  -0.030746065683   0.66310359       0.0000       0.0000 0.0032
## [705,]  -0.013508532989   0.29500978       0.0000       0.0000 0.0028
## [706,]  -0.002214658920   0.55678281       0.0000       0.0000 0.0048
## [707,]  -0.003227728786   0.14044609       0.0000       0.0000 0.0012
## [708,]  -0.025124426510   0.56978955       0.0000       0.0000 0.0044
## [709,]  -0.011770054975   0.33177240       0.0000       0.0000 0.0032
## [710,]  -0.008673496365   0.24258536       0.0000       0.0000 0.0056

4.2.4 Predict fitted values for each individual

pred.npb <- predict(fit.npb)
fittedvals <- pred.npb$fitted.vals

4.2.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals, Y)
abline(a = 0, b = 1, col = "red")

4.3 Run the NPB model with temperaure and ozone

Below I’ve used the set of priors labeled “24” and set scaleY = T

The priors are as follows: r priors.npb.24

Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.

priors.npb <- priors.npb.24

#' Exposures (minus temperature)
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v4.2.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4.2.rdata"))
npb.sum2 <- summary(fit.npb2)

4.3.1 First, main effect regression coefficients with PIPs

rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                -2.39072192  9.792126   -29.271869     8.534157 0.3064
## mean_o3                -6.38650708 23.092058   -65.112302     6.938996 0.3712
## mean_temp              13.08988731 48.534890   -18.587026   189.293128 0.3804
## pct_tree_cover         -0.35132165  5.328952   -12.137421    11.560674 0.2528
## pct_impervious         -0.71579581  5.075087   -14.363937     7.427655 0.2476
## mean_aadt_intensity     0.70135685  5.889176    -8.973130    18.216043 0.2392
## dist_m_tri             -1.09951786  6.231821   -18.891336     8.900200 0.2728
## dist_m_npl             -0.01654537  6.339152   -11.705638    14.574608 0.2604
## dist_m_waste_site       3.02530578 10.570529    -7.380639    39.172809 0.3056
## dist_m_major_emit       0.04946465  5.249829   -10.655397    13.058661 0.2368
## dist_m_cafo            -2.08149176 15.148641   -31.012868    14.249976 0.3364
## dist_m_mine_well       -1.72250145  7.385683   -22.594290     8.900200 0.3096
## cvd_rate_adj           -1.39496856  6.112685   -18.356038     5.931195 0.2764
## res_rate_adj           -2.46954801  7.830513   -26.805916     4.985631 0.3028
## violent_crime_rate     -0.28237724  5.442212   -12.212582     9.176109 0.2544
## property_crime_rate    -1.45733604  5.778188   -18.269563     5.210600 0.2768
## pct_less_hs            -1.11592115  7.050666   -17.899684    10.643142 0.2916
## pct_unemp              -6.62599040 14.516231   -51.310175     2.495315 0.3968
## pct_limited_eng        -1.01024567  5.640255   -16.184771     6.906877 0.2500
## pct_hh_pov             -1.06713407  5.614263   -14.965020     6.580130 0.2624
## pct_poc                -0.54972375  5.929487   -13.117756    12.632636 0.2596

4.3.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum2$interactions
##          Posterior Mean           SD 95% CI Lower 95% CI Upper    PIP
##   [1,]    1.51232500652   9.77946055       0.0000     22.15511 0.0280
##   [2,]    0.65433959400   6.19129299       0.0000      0.00000 0.0168
##   [3,]   -0.00326218467   0.42473806       0.0000      0.00000 0.0020
##   [4,]   -0.00698232110   0.20080980       0.0000      0.00000 0.0044
##   [5,]   -0.00258271102   0.46337225       0.0000      0.00000 0.0032
##   [6,]   -0.01465786232   0.37900692       0.0000      0.00000 0.0028
##   [7,]   -0.00076245021   0.24923364       0.0000      0.00000 0.0020
##   [8,]   -0.01720915634   0.58394565       0.0000      0.00000 0.0024
##   [9,]    0.00051688821   0.18588148       0.0000      0.00000 0.0024
##  [10,]   -0.00413202603   0.27656153       0.0000      0.00000 0.0028
##  [11,]   -0.02641565249   0.83446506       0.0000      0.00000 0.0040
##  [12,]   -0.00201949522   0.20727279       0.0000      0.00000 0.0016
##  [13,]   -0.01572387134   0.43302019       0.0000      0.00000 0.0044
##  [14,]   -0.03420576925   0.93587891       0.0000      0.00000 0.0040
##  [15,]   -0.00887746095   0.38409965       0.0000      0.00000 0.0016
##  [16,]   -0.02717263934   0.84536743       0.0000      0.00000 0.0052
##  [17,]   -0.00915469747   0.31542677       0.0000      0.00000 0.0016
##  [18,]   -0.05213203027   1.21569385       0.0000      0.00000 0.0044
##  [19,]   -0.01989527242   0.53419496       0.0000      0.00000 0.0032
##  [20,]    0.00265653965   0.34603287       0.0000      0.00000 0.0040
##  [21,] -162.01330438843  30.03114028    -242.3003   -117.79902 1.0000
##  [22,]   -0.01184325393   0.51146950       0.0000      0.00000 0.0036
##  [23,]   -0.01581913441   0.40541897       0.0000      0.00000 0.0044
##  [24,]   -0.00175063397   0.12828228       0.0000      0.00000 0.0024
##  [25,]   -0.06190253022   1.13458263       0.0000      0.00000 0.0052
##  [26,]   -0.01826842294   0.42458788       0.0000      0.00000 0.0024
##  [27,]   -0.06284083126   1.26441921       0.0000      0.00000 0.0048
##  [28,]   -0.01405008554   0.45123778       0.0000      0.00000 0.0044
##  [29,]   -0.01392133355   0.58023036       0.0000      0.00000 0.0060
##  [30,]   -0.03418771444   0.82919139       0.0000      0.00000 0.0064
##  [31,]   -0.00195478053   0.27756505       0.0000      0.00000 0.0028
##  [32,]   -0.01533309382   0.34615416       0.0000      0.00000 0.0036
##  [33,]   -0.00246924398   0.39391033       0.0000      0.00000 0.0020
##  [34,]   -0.00077100846   0.32513796       0.0000      0.00000 0.0036
##  [35,]    0.03361347817   0.98484019       0.0000      0.00000 0.0032
##  [36,]   -0.00263500578   0.44359110       0.0000      0.00000 0.0036
##  [37,]   -0.00772861063   0.21683726       0.0000      0.00000 0.0028
##  [38,]    0.03076925176   1.01178640       0.0000      0.00000 0.0048
##  [39,]   -0.00636780945   0.21659277       0.0000      0.00000 0.0024
##  [40,]   -0.00870161813   0.24276099       0.0000      0.00000 0.0032
##  [41,]   -0.00237384931   0.39054599       0.0000      0.00000 0.0028
##  [42,]   -0.01033005846   0.46109399       0.0000      0.00000 0.0024
##  [43,]   -0.00865241668   0.39733920       0.0000      0.00000 0.0016
##  [44,]   -0.01836745693   0.50492526       0.0000      0.00000 0.0028
##  [45,]   -0.04265413398   0.99815333       0.0000      0.00000 0.0056
##  [46,]   -0.01578110771   0.34818414       0.0000      0.00000 0.0040
##  [47,]   -0.06662207191   1.17559537       0.0000      0.00000 0.0064
##  [48,]   -0.01948388433   0.53321135       0.0000      0.00000 0.0036
##  [49,]    0.01931485945   1.08014670       0.0000      0.00000 0.0040
##  [50,]   -0.00847375822   0.36105790       0.0000      0.00000 0.0032
##  [51,]   -0.04065556367   0.84588285       0.0000      0.00000 0.0040
##  [52,]    0.00081360093   0.23351018       0.0000      0.00000 0.0036
##  [53,]    0.00330232150   0.31501878       0.0000      0.00000 0.0024
##  [54,]    0.00215118747   0.28332544       0.0000      0.00000 0.0016
##  [55,]   -0.02386347007   0.63630564       0.0000      0.00000 0.0028
##  [56,]    0.00888292132   0.58780776       0.0000      0.00000 0.0028
##  [57,]    0.00516728824   0.50140297       0.0000      0.00000 0.0036
##  [58,]    0.00680777122   0.34714313       0.0000      0.00000 0.0032
##  [59,]   -0.01113713531   0.47136232       0.0000      0.00000 0.0032
##  [60,]   -0.00428069893   0.48079407       0.0000      0.00000 0.0028
##  [61,]   -0.00181055679   0.19579166       0.0000      0.00000 0.0036
##  [62,]   -0.00929964925   0.39727476       0.0000      0.00000 0.0036
##  [63,]   -0.00076246961   0.24012954       0.0000      0.00000 0.0012
##  [64,]   -0.01399946919   0.43425929       0.0000      0.00000 0.0044
##  [65,]   -0.01834968197   0.60942497       0.0000      0.00000 0.0024
##  [66,]   -0.01676568762   0.45907003       0.0000      0.00000 0.0024
##  [67,]    0.00873250723   0.35072876       0.0000      0.00000 0.0032
##  [68,]   -0.03112746884   0.58896286       0.0000      0.00000 0.0040
##  [69,]   -0.00916907282   0.26212941       0.0000      0.00000 0.0048
##  [70,]   -0.00274249181   0.28049818       0.0000      0.00000 0.0024
##  [71,]   -0.00664142171   0.28458463       0.0000      0.00000 0.0028
##  [72,]   -0.00148415588   0.49367543       0.0000      0.00000 0.0040
##  [73,]   -0.00643607825   0.14760824       0.0000      0.00000 0.0020
##  [74,]    0.00377571198   0.26397622       0.0000      0.00000 0.0016
##  [75,]    0.02172002175   0.94570698       0.0000      0.00000 0.0028
##  [76,]    0.00262002602   0.26316336       0.0000      0.00000 0.0016
##  [77,]   -0.00266481974   0.14267675       0.0000      0.00000 0.0012
##  [78,]   -0.00931016756   0.32417618       0.0000      0.00000 0.0024
##  [79,]   -0.00417412081   0.15643635       0.0000      0.00000 0.0020
##  [80,]   -0.02991328465   0.69868188       0.0000      0.00000 0.0040
##  [81,]   -0.00400435943   0.16112114       0.0000      0.00000 0.0024
##  [82,]   -0.01134694833   0.44650688       0.0000      0.00000 0.0044
##  [83,]   -0.01470208235   0.64314774       0.0000      0.00000 0.0056
##  [84,]    0.00081685361   0.16316647       0.0000      0.00000 0.0024
##  [85,]   -0.01692101990   0.42458312       0.0000      0.00000 0.0052
##  [86,]   -0.00303183919   0.28172817       0.0000      0.00000 0.0024
##  [87,]   -0.01170225916   0.29534472       0.0000      0.00000 0.0028
##  [88,]    0.00420829688   0.14886311       0.0000      0.00000 0.0024
##  [89,]   -0.00088260938   0.50156149       0.0000      0.00000 0.0020
##  [90,]   -0.00034225134   0.29047439       0.0000      0.00000 0.0016
##  [91,]    0.01520545592   1.02976610       0.0000      0.00000 0.0040
##  [92,]   -0.01090466974   0.46568562       0.0000      0.00000 0.0036
##  [93,]    0.00698140330   0.37160472       0.0000      0.00000 0.0028
##  [94,]    0.01026513174   0.72036309       0.0000      0.00000 0.0036
##  [95,]    0.01186377041   0.89584271       0.0000      0.00000 0.0040
##  [96,]   -0.01370326930   0.50860747       0.0000      0.00000 0.0036
##  [97,]    0.00884292445   0.26344459       0.0000      0.00000 0.0036
##  [98,]   -0.00499081786   0.48085344       0.0000      0.00000 0.0048
##  [99,]   -0.04935898799   1.12275729       0.0000      0.00000 0.0044
## [100,]   -0.00525564840   0.15522825       0.0000      0.00000 0.0012
## [101,]   -0.00342111130   0.49868951       0.0000      0.00000 0.0024
## [102,]   -0.00167965421   0.32040909       0.0000      0.00000 0.0032
## [103,]   -0.01639051845   0.39085494       0.0000      0.00000 0.0028
## [104,]   -0.00328834861   0.51811731       0.0000      0.00000 0.0044
## [105,]    0.00181060566   0.62539168       0.0000      0.00000 0.0064
## [106,]   -0.01042117773   0.31056470       0.0000      0.00000 0.0040
## [107,]    0.00392550021   0.87337660       0.0000      0.00000 0.0060
## [108,]   -0.00496647687   0.25049836       0.0000      0.00000 0.0028
## [109,]    0.00214169967   0.34043384       0.0000      0.00000 0.0032
## [110,]   -0.00843346615   0.38649939       0.0000      0.00000 0.0036
## [111,]    0.04283338443   1.28890391       0.0000      0.00000 0.0044
## [112,]    0.00131770015   0.24019785       0.0000      0.00000 0.0016
## [113,]   -0.01415473092   0.54284465       0.0000      0.00000 0.0012
## [114,]   -0.00468269599   0.21427685       0.0000      0.00000 0.0024
## [115,]    0.02742063366   0.99934642       0.0000      0.00000 0.0028
## [116,]    0.00213400076   0.26318122       0.0000      0.00000 0.0024
## [117,]    0.09451353113   2.11419722       0.0000      0.00000 0.0052
## [118,]    0.01125068479   0.30564230       0.0000      0.00000 0.0020
## [119,]   -0.00120453843   0.18989642       0.0000      0.00000 0.0024
## [120,]   -0.01011594535   0.45805778       0.0000      0.00000 0.0024
## [121,]   -0.00455307834   0.35418178       0.0000      0.00000 0.0032
## [122,]   -0.00104005300   0.22495820       0.0000      0.00000 0.0024
## [123,]   -0.00812531898   0.38244120       0.0000      0.00000 0.0024
## [124,]   -0.00955384408   0.36604374       0.0000      0.00000 0.0028
## [125,]   -0.00088533708   0.25308010       0.0000      0.00000 0.0024
## [126,]   -0.00688773663   0.19236912       0.0000      0.00000 0.0032
## [127,]   -0.00093408541   0.21823578       0.0000      0.00000 0.0032
## [128,]   -0.00863485257   0.41925571       0.0000      0.00000 0.0028
## [129,]   -0.02182768695   0.56599932       0.0000      0.00000 0.0032
## [130,]    0.00871174852   0.43010392       0.0000      0.00000 0.0028
## [131,]   -0.00306415996   0.26639942       0.0000      0.00000 0.0028
## [132,]   -0.00014821033   0.31484462       0.0000      0.00000 0.0024
## [133,]   -0.00248091846   0.29610804       0.0000      0.00000 0.0024
## [134,]    0.00255497739   0.16443930       0.0000      0.00000 0.0028
## [135,]    0.02477850202   0.80650181       0.0000      0.00000 0.0040
## [136,]   -0.00585207553   0.50004908       0.0000      0.00000 0.0032
## [137,]   -0.01754375422   0.50322545       0.0000      0.00000 0.0032
## [138,]   -0.00635157790   0.47202398       0.0000      0.00000 0.0048
## [139,]   -0.00675954612   0.34257534       0.0000      0.00000 0.0028
## [140,]   -0.02892078421   0.73719980       0.0000      0.00000 0.0036
## [141,]   -0.00325157028   0.17715220       0.0000      0.00000 0.0020
## [142,]    0.00170712807   0.29965516       0.0000      0.00000 0.0020
## [143,]   -0.00396005182   0.24704629       0.0000      0.00000 0.0032
## [144,]    0.00104541599   0.33441344       0.0000      0.00000 0.0040
## [145,]    0.02632393771   0.79304805       0.0000      0.00000 0.0044
## [146,]    0.11453877198   2.24724014       0.0000      0.00000 0.0084
## [147,]   -0.00118337408   0.18467013       0.0000      0.00000 0.0024
## [148,]   -0.01954895394   0.59439195       0.0000      0.00000 0.0028
## [149,]   -0.01563510737   0.51490902       0.0000      0.00000 0.0028
## [150,]   -0.02274028100   1.14776307       0.0000      0.00000 0.0036
## [151,]   -0.03632502861   0.90199192       0.0000      0.00000 0.0040
## [152,]   -0.02447586000   0.56375518       0.0000      0.00000 0.0056
## [153,]   -0.01167650517   0.56763647       0.0000      0.00000 0.0040
## [154,]   -0.02848551807   0.66834145       0.0000      0.00000 0.0048
## [155,]   -0.01107455772   0.57786553       0.0000      0.00000 0.0048
## [156,]   -0.06620619539   1.33514020       0.0000      0.00000 0.0040
## [157,]   -0.00085058322   0.21320901       0.0000      0.00000 0.0032
## [158,]   -0.02397096839   0.77821208       0.0000      0.00000 0.0040
## [159,]   -0.01406526385   0.43620517       0.0000      0.00000 0.0024
## [160,]   -0.02960082230   0.75126590       0.0000      0.00000 0.0052
## [161,]   -0.00083185121   0.04159256       0.0000      0.00000 0.0004
## [162,]   -0.00035243936   0.27456567       0.0000      0.00000 0.0032
## [163,]    0.00053194901   0.23622017       0.0000      0.00000 0.0032
## [164,]    0.00791101714   0.37012824       0.0000      0.00000 0.0032
## [165,]    0.02144697876   0.95508054       0.0000      0.00000 0.0024
## [166,]   -0.00650048524   0.74282353       0.0000      0.00000 0.0056
## [167,]   -0.01428402607   0.32297750       0.0000      0.00000 0.0036
## [168,]    0.00083027082   0.10202641       0.0000      0.00000 0.0020
## [169,]   -0.01195829852   0.30887801       0.0000      0.00000 0.0032
## [170,]    0.00754533847   0.70904933       0.0000      0.00000 0.0028
## [171,]    0.00396747296   0.21114662       0.0000      0.00000 0.0012
## [172,]    0.40468620159   5.83831442       0.0000      0.00000 0.0084
## [173,]    0.03416647705   1.39886457       0.0000      0.00000 0.0032
## [174,]    0.00528398808   0.27424546       0.0000      0.00000 0.0036
## [175,]   -0.01168584342   0.64591621       0.0000      0.00000 0.0032
## [176,]   -0.00225641816   0.19584860       0.0000      0.00000 0.0024
## [177,]   -0.01847656373   0.43483400       0.0000      0.00000 0.0044
## [178,]   -0.00136325961   0.34222873       0.0000      0.00000 0.0024
## [179,]   -0.07861519243   1.38447855       0.0000      0.00000 0.0052
## [180,]   -0.01766687592   0.58316294       0.0000      0.00000 0.0020
## [181,]   -0.05449940027   1.34580673       0.0000      0.00000 0.0044
## [182,]   -0.00550865719   0.45359948       0.0000      0.00000 0.0040
## [183,]   -0.00753767624   0.35442525       0.0000      0.00000 0.0024
## [184,]   -0.01648485042   0.55550000       0.0000      0.00000 0.0032
## [185,]    0.00061007634   0.02042972       0.0000      0.00000 0.0012
## [186,]   -0.01537272559   0.58014398       0.0000      0.00000 0.0056
## [187,]   -0.02425623563   0.64797846       0.0000      0.00000 0.0048
## [188,]   -0.02614081735   0.64294469       0.0000      0.00000 0.0048
## [189,]    0.00379131831   0.32058320       0.0000      0.00000 0.0008
## [190,]   -0.00620099566   0.15167889       0.0000      0.00000 0.0032
## [191,]    0.01369112583   0.57626531       0.0000      0.00000 0.0040
## [192,]    0.00020014000   0.10985784       0.0000      0.00000 0.0016
## [193,]   -0.01133432670   0.33995063       0.0000      0.00000 0.0040
## [194,]   -0.00229279442   0.09903369       0.0000      0.00000 0.0024
## [195,]   -0.00465513097   0.19763594       0.0000      0.00000 0.0028
## [196,]    0.00088303588   0.31844784       0.0000      0.00000 0.0020
## [197,]   -0.00160604559   0.25418101       0.0000      0.00000 0.0032
## [198,]   -0.00078324722   0.31464538       0.0000      0.00000 0.0024
## [199,]   -0.01874556379   0.38671817       0.0000      0.00000 0.0048
## [200,]   -0.01316330074   0.58228591       0.0000      0.00000 0.0052
## [201,]    0.00698627041   0.54577406       0.0000      0.00000 0.0036
## [202,]   -0.00609916009   0.21849502       0.0000      0.00000 0.0044
## [203,]    0.00068748547   0.29077321       0.0000      0.00000 0.0020
## [204,]    0.01577490865   0.71470939       0.0000      0.00000 0.0032
## [205,]   -0.01756494189   0.48562814       0.0000      0.00000 0.0028
## [206,]   -0.01623695480   0.39064585       0.0000      0.00000 0.0036
## [207,]   -0.00851878570   0.23177510       0.0000      0.00000 0.0020
## [208,]   -0.00555952246   0.28823686       0.0000      0.00000 0.0032
## [209,]   -0.01310882016   0.33090059       0.0000      0.00000 0.0036
## [210,]    0.00397439002   0.36160972       0.0000      0.00000 0.0028
## [211,]    0.01181076670   0.64145577       0.0000      0.00000 0.0024
## [212,]   -0.00263521844   0.35464769       0.0000      0.00000 0.0016
## [213,]   -0.03369827965   0.64249389       0.0000      0.00000 0.0048
## [214,]    0.02120719366   0.94044337       0.0000      0.00000 0.0036
## [215,]   -0.00649825751   0.30579001       0.0000      0.00000 0.0040
## [216,]   -0.06697035496   2.91963793       0.0000      0.00000 0.0040
## [217,]    0.00577287167   1.20139247       0.0000      0.00000 0.0024
## [218,]   -0.00893031198   0.26073922       0.0000      0.00000 0.0024
## [219,]   -0.09907518889   1.92078043       0.0000      0.00000 0.0052
## [220,]    0.01684645064   0.94558437       0.0000      0.00000 0.0032
## [221,]   -0.42689185453   8.96141211       0.0000      0.00000 0.0084
## [222,]   -0.13343653112   3.27307413       0.0000      0.00000 0.0044
## [223,]   -0.00474497547   0.13280587       0.0000      0.00000 0.0016
## [224,]    0.04622995410   1.49138032       0.0000      0.00000 0.0020
## [225,]   -0.09013857287   3.20483813       0.0000      0.00000 0.0056
## [226,]   -0.68575241664   9.93684301       0.0000      0.00000 0.0092
## [227,]   -0.84811520783  11.15975695       0.0000      0.00000 0.0088
## [228,]   -0.02172286442   0.63544685       0.0000      0.00000 0.0024
## [229,]    0.05579322715   1.90206447       0.0000      0.00000 0.0060
## [230,]   -0.84511038806  10.85259135       0.0000      0.00000 0.0096
## [231,]    0.00295614029   0.28163114       0.0000      0.00000 0.0028
## [232,]   -0.26777839017   5.83786198       0.0000      0.00000 0.0044
## [233,]   -0.01959915470   0.69018149       0.0000      0.00000 0.0024
## [234,]    0.03586039801   1.00692544       0.0000      0.00000 0.0028
## [235,]    0.01466778855   0.84478091       0.0000      0.00000 0.0044
## [236,]   -0.01391118389   0.66483515       0.0000      0.00000 0.0044
## [237,]   -0.00016257388   0.22740965       0.0000      0.00000 0.0020
## [238,]   -0.00850262111   0.31175005       0.0000      0.00000 0.0020
## [239,]   -0.03235314422   0.70199458       0.0000      0.00000 0.0040
## [240,]   -0.01483209147   0.37465962       0.0000      0.00000 0.0028
## [241,]   -0.02060320426   0.60025856       0.0000      0.00000 0.0036
## [242,]    0.00965079661   0.90217988       0.0000      0.00000 0.0028
## [243,]   -0.04645760271   1.85778054       0.0000      0.00000 0.0036
## [244,]   -0.01908747531   0.57788992       0.0000      0.00000 0.0028
## [245,]   -0.02475873455   1.07326277       0.0000      0.00000 0.0028
## [246,]   -0.00864603094   0.35670066       0.0000      0.00000 0.0032
## [247,]    0.04250479129   1.41723874       0.0000      0.00000 0.0036
## [248,]   -0.08371752681   2.15643179       0.0000      0.00000 0.0044
## [249,]   -0.01611106755   0.83745933       0.0000      0.00000 0.0028
## [250,]   -0.08295782627   3.41117442       0.0000      0.00000 0.0040
## [251,]   -0.01427302222   0.91650341       0.0000      0.00000 0.0052
## [252,]  -17.06813688192  60.99198737    -241.6339      0.00000 0.0764
## [253,]   -0.04263101963   3.26016327       0.0000      0.00000 0.0036
## [254,]   -0.16106158359   4.37083575       0.0000      0.00000 0.0064
## [255,]    0.18912261934   4.45863306       0.0000      0.00000 0.0044
## [256,]   -0.06092328628   1.55745976       0.0000      0.00000 0.0052
## [257,]   -0.03323842632   0.80544301       0.0000      0.00000 0.0036
## [258,]   -0.05752349805   2.41681394       0.0000      0.00000 0.0036
## [259,]   -0.03530989120   0.98952110       0.0000      0.00000 0.0068
## [260,]    0.00944223481   0.35789962       0.0000      0.00000 0.0044
## [261,]    0.03027872071   1.04198189       0.0000      0.00000 0.0048
## [262,]    0.01274473146   0.75615019       0.0000      0.00000 0.0028
## [263,]    0.01829130003   0.80827983       0.0000      0.00000 0.0024
## [264,]    0.02055560200   0.84492115       0.0000      0.00000 0.0020
## [265,]   -0.01308331228   0.47308671       0.0000      0.00000 0.0036
## [266,]   -0.02012958765   0.63270556       0.0000      0.00000 0.0040
## [267,]   -0.01984260211   0.90078021       0.0000      0.00000 0.0028
## [268,]    0.01944100431   1.05061745       0.0000      0.00000 0.0040
## [269,]   -0.02756198636   0.59713260       0.0000      0.00000 0.0036
## [270,]   -1.82166863816  15.32185389       0.0000      0.00000 0.0172
## [271,]    0.02320974158   1.07335461       0.0000      0.00000 0.0036
## [272,]   -0.01024682517   0.62893520       0.0000      0.00000 0.0020
## [273,]    0.48754298194   9.92341005       0.0000      0.00000 0.0060
## [274,]   -0.15934859364   4.04254047       0.0000      0.00000 0.0044
## [275,]   -0.03474553656   0.66787819       0.0000      0.00000 0.0044
## [276,]   -0.38486413705   7.02508755       0.0000      0.00000 0.0060
## [277,]  -84.08581551146 119.50624294    -435.5029      0.00000 0.4056
## [278,]    0.16533069265   4.70393551       0.0000      0.00000 0.0044
## [279,]   -0.39831054329   8.33013771       0.0000      0.00000 0.0068
## [280,]   -0.18773712067   4.50828068       0.0000      0.00000 0.0052
## [281,]    8.73297867917  33.88649659       0.0000    136.11390 0.0708
## [282,]   -0.32842423179   6.69193519       0.0000      0.00000 0.0048
## [283,]   -0.00623063015   0.25726221       0.0000      0.00000 0.0048
## [284,]   -0.05297042854   1.42566071       0.0000      0.00000 0.0044
## [285,]   -0.01288708571   0.50383818       0.0000      0.00000 0.0020
## [286,]    0.12010753087   2.41582708       0.0000      0.00000 0.0052
## [287,]    0.00195790578   0.40985050       0.0000      0.00000 0.0036
## [288,]   -0.00091914882   0.27654710       0.0000      0.00000 0.0012
## [289,]   -0.01540880613   0.52225567       0.0000      0.00000 0.0028
## [290,]   -0.01240462075   0.55804351       0.0000      0.00000 0.0044
## [291,]   -0.00508414125   0.19895193       0.0000      0.00000 0.0028
## [292,]   -0.01121379641   0.21422227       0.0000      0.00000 0.0032
## [293,]   -0.02452916577   0.63580031       0.0000      0.00000 0.0036
## [294,]   -0.00086443966   0.66878661       0.0000      0.00000 0.0036
## [295,]    0.04372259758   2.15298497       0.0000      0.00000 0.0036
## [296,]    0.01537738037   1.42585729       0.0000      0.00000 0.0020
## [297,]    0.03875977354   1.22183588       0.0000      0.00000 0.0020
## [298,]   -0.00383336987   0.39126241       0.0000      0.00000 0.0048
## [299,]   -0.19844581441   5.31453182       0.0000      0.00000 0.0056
## [300,]   -0.02604347688   0.61266029       0.0000      0.00000 0.0044
## [301,]    0.04181779241   1.57792018       0.0000      0.00000 0.0032
## [302,]    0.00614189857   0.46428208       0.0000      0.00000 0.0024
## [303,]   -0.00568273876   0.25544356       0.0000      0.00000 0.0024
## [304,]    0.02350433529   1.28341105       0.0000      0.00000 0.0040
## [305,]   -0.01356058497   0.60078222       0.0000      0.00000 0.0040
## [306,]    0.05175908112   1.78167464       0.0000      0.00000 0.0028
## [307,]   -0.03930125302   1.05606095       0.0000      0.00000 0.0020
## [308,]   -0.00491509506   0.19825466       0.0000      0.00000 0.0032
## [309,]   -0.03557774564   1.05732730       0.0000      0.00000 0.0044
## [310,]   -0.07443133873   2.79798463       0.0000      0.00000 0.0044
## [311,]   -0.00996304992   0.25734367       0.0000      0.00000 0.0020
## [312,]   -0.00235239913   0.43006491       0.0000      0.00000 0.0048
## [313,]   -0.00100184816   0.10444407       0.0000      0.00000 0.0016
## [314,]   -0.02385692402   0.59735421       0.0000      0.00000 0.0048
## [315,]   -0.00554029173   0.43264355       0.0000      0.00000 0.0020
## [316,]   -0.01110005543   0.37749704       0.0000      0.00000 0.0032
## [317,]   -0.00517453570   0.33026005       0.0000      0.00000 0.0024
## [318,]    0.02321385147   1.56467120       0.0000      0.00000 0.0028
## [319,]    0.00149862921   0.12522474       0.0000      0.00000 0.0024
## [320,]    0.02353950774   1.02543638       0.0000      0.00000 0.0020
## [321,]    0.04555568873   2.13810572       0.0000      0.00000 0.0024
## [322,]    0.03634392220   1.38118012       0.0000      0.00000 0.0028
## [323,]   -0.00682981972   0.29949131       0.0000      0.00000 0.0032
## [324,]   -0.02589556712   0.58418188       0.0000      0.00000 0.0040
## [325,]   -0.22891554579   5.21971524       0.0000      0.00000 0.0072
## [326,]   -0.01427500288   0.28085857       0.0000      0.00000 0.0036
## [327,]    0.00389442064   0.81670582       0.0000      0.00000 0.0048
## [328,]   -0.01602007175   1.31439873       0.0000      0.00000 0.0044
## [329,]   -0.01254563367   0.45043473       0.0000      0.00000 0.0028
## [330,]   -0.01345356656   0.50353280       0.0000      0.00000 0.0024
## [331,]   -0.00486420157   0.62495683       0.0000      0.00000 0.0036
## [332,]   -0.01221946364   0.25943804       0.0000      0.00000 0.0024
## [333,]   -0.00255666221   0.33369935       0.0000      0.00000 0.0040
## [334,]   -0.00316175096   0.52063744       0.0000      0.00000 0.0044
## [335,]   -0.05176015298   1.12161865       0.0000      0.00000 0.0056
## [336,]   -0.00152301729   0.30611755       0.0000      0.00000 0.0028
## [337,]    0.01199926836   1.01544410       0.0000      0.00000 0.0020
## [338,]   -0.02361682784   0.90920435       0.0000      0.00000 0.0040
## [339,]   -0.01560294366   0.44405678       0.0000      0.00000 0.0036
## [340,]   -0.04008597096   0.80583714       0.0000      0.00000 0.0040
## [341,]    0.00008155388   0.40422865       0.0000      0.00000 0.0036
## [342,]   -0.00826613236   0.18611027       0.0000      0.00000 0.0024
## [343,]   -0.01489730540   0.34147453       0.0000      0.00000 0.0032
## [344,]    0.01554023949   0.86924998       0.0000      0.00000 0.0040
## [345,]   -0.03109029204   0.80956269       0.0000      0.00000 0.0052
## [346,]   -0.01644030358   0.54455987       0.0000      0.00000 0.0024
## [347,]    0.30811492790   6.07403000       0.0000      0.00000 0.0052
## [348,]    0.04809574926   2.79829775       0.0000      0.00000 0.0032
## [349,]   -0.02339147623   0.79666212       0.0000      0.00000 0.0032
## [350,]   -0.02264447355   0.85841558       0.0000      0.00000 0.0048
## [351,]   -0.07386603216   4.00262116       0.0000      0.00000 0.0052
## [352,]   -0.05156932060   1.13034783       0.0000      0.00000 0.0044
## [353,]    0.04179753994   2.48560684       0.0000      0.00000 0.0024
## [354,]    0.01311048004   0.85125381       0.0000      0.00000 0.0028
## [355,]    0.00163827068   0.27257368       0.0000      0.00000 0.0016
## [356,]   -0.00456897900   0.31323511       0.0000      0.00000 0.0028
## [357,]   -0.01474653390   0.40884402       0.0000      0.00000 0.0040
## [358,]    0.01723973420   0.51101819       0.0000      0.00000 0.0052
## [359,]   -0.01824347167   0.62482277       0.0000      0.00000 0.0032
## [360,]    0.02259502369   1.11900619       0.0000      0.00000 0.0028
## [361,]   -0.07767608877   1.40126687       0.0000      0.00000 0.0060
## [362,]   -0.03465040927   1.12437601       0.0000      0.00000 0.0020
## [363,]   -0.02686270737   0.75670053       0.0000      0.00000 0.0044
## [364,]   -0.00621256603   0.26191506       0.0000      0.00000 0.0040
## [365,]    0.00038694325   0.18282424       0.0000      0.00000 0.0032
## [366,]    0.00128874927   0.38256275       0.0000      0.00000 0.0032
## [367,]    0.00508961063   0.33667368       0.0000      0.00000 0.0028
## [368,]   -0.01400608712   0.45144010       0.0000      0.00000 0.0032
## [369,]   -0.01936867749   0.46854493       0.0000      0.00000 0.0032
## [370,]    0.00946998355   1.24716654       0.0000      0.00000 0.0048
## [371,]   -0.00608234363   0.41888949       0.0000      0.00000 0.0044
## [372,]    0.00041428604   0.32108543       0.0000      0.00000 0.0028
## [373,]    0.14667595968   3.92324873       0.0000      0.00000 0.0076
## [374,]   -0.00625137561   1.00146266       0.0000      0.00000 0.0060
## [375,]   -0.00635180388   0.95506048       0.0000      0.00000 0.0044
## [376,]   -0.01425609405   0.57847365       0.0000      0.00000 0.0036
## [377,]   -0.63229532731  11.03494739       0.0000      0.00000 0.0072
## [378,]    0.00169857308   0.37026475       0.0000      0.00000 0.0036
## [379,]    0.00730737062   0.33220713       0.0000      0.00000 0.0032
## [380,]    0.01591659740   1.47675146       0.0000      0.00000 0.0056
## [381,]   -0.00674407797   0.18219895       0.0000      0.00000 0.0020
## [382,]    0.12074595685   2.79467910       0.0000      0.00000 0.0052
## [383,]    0.06014826916   1.88593632       0.0000      0.00000 0.0048
## [384,]    0.03522703166   1.19956791       0.0000      0.00000 0.0036
## [385,]    0.00618270076   1.04414700       0.0000      0.00000 0.0060
## [386,]    0.02145413895   1.42781385       0.0000      0.00000 0.0024
## [387,]   -0.01690552186   0.46104393       0.0000      0.00000 0.0044
## [388,]   -0.01807413873   1.25475436       0.0000      0.00000 0.0032
## [389,]   -0.01766683045   0.38528185       0.0000      0.00000 0.0040
## [390,]   -0.00447146050   0.60494527       0.0000      0.00000 0.0044
## [391,]   -0.03070680152   0.74188613       0.0000      0.00000 0.0036
## [392,]    0.01322252860   0.55187259       0.0000      0.00000 0.0028
## [393,]   -0.00114215634   0.29559087       0.0000      0.00000 0.0032
## [394,]   -0.00747522441   0.42159227       0.0000      0.00000 0.0040
## [395,]   -0.00576893732   0.20141490       0.0000      0.00000 0.0020
## [396,]   -0.00487925082   0.63477309       0.0000      0.00000 0.0036
## [397,]   -0.00872991502   1.23258949       0.0000      0.00000 0.0028
## [398,]   -0.01577947337   0.66172313       0.0000      0.00000 0.0036
## [399,]    0.03107481555   1.49657056       0.0000      0.00000 0.0044
## [400,]   -0.00312862118   0.17424294       0.0000      0.00000 0.0020
## [401,]   -0.01245307846   0.70777420       0.0000      0.00000 0.0040
## [402,]   -0.01195719429   1.04202788       0.0000      0.00000 0.0032
## [403,]   -0.03627356584   3.62048169       0.0000      0.00000 0.0036
## [404,]   -0.00055545952   0.28886136       0.0000      0.00000 0.0028
## [405,]    0.01040056577   0.78870461       0.0000      0.00000 0.0040
## [406,]   -0.01341921312   0.46417288       0.0000      0.00000 0.0020
## [407,]   -0.00700091733   0.29594287       0.0000      0.00000 0.0032
## [408,]   -0.01394192199   0.59436301       0.0000      0.00000 0.0040
## [409,]    0.01121040201   1.10693277       0.0000      0.00000 0.0036
## [410,]   -0.01026527195   0.23924833       0.0000      0.00000 0.0028
## [411,]   -0.04559763799   1.24849376       0.0000      0.00000 0.0028
## [412,]    0.00342130931   0.17106547       0.0000      0.00000 0.0004
## [413,]   -0.00580549815   0.13515868       0.0000      0.00000 0.0020
## [414,]    0.02608670703   1.78848866       0.0000      0.00000 0.0044
## [415,]   -1.58585394105  14.72076454       0.0000      0.00000 0.0168
## [416,]   -0.00036515105   0.22599677       0.0000      0.00000 0.0036
## [417,]   -0.12333977393   2.16129268       0.0000      0.00000 0.0080
## [418,]    0.03282482884   1.35796383       0.0000      0.00000 0.0040
## [419,]   -0.03402209521   0.77184841       0.0000      0.00000 0.0044
## [420,]   -0.00564093853   0.15866455       0.0000      0.00000 0.0020
## [421,]    0.00124065922   0.38482791       0.0000      0.00000 0.0020
## [422,]    0.00353012502   0.51902551       0.0000      0.00000 0.0032
## [423,]    0.04583850520   2.11955473       0.0000      0.00000 0.0028
## [424,]   -0.00017131910   0.57495642       0.0000      0.00000 0.0032
## [425,]    0.00282219945   0.29057347       0.0000      0.00000 0.0028
## [426,]    0.22832251239   4.31052512       0.0000      0.00000 0.0076
## [427,]   -0.00227137980   1.00257968       0.0000      0.00000 0.0044
## [428,]    0.00323405601   0.29914527       0.0000      0.00000 0.0028
## [429,]   -0.31917951950   6.86986724       0.0000      0.00000 0.0044
## [430,]    0.00581479650   0.73538565       0.0000      0.00000 0.0040
## [431,]   -0.02102638829   0.41917055       0.0000      0.00000 0.0040
## [432,]    0.09184018655   2.50181581       0.0000      0.00000 0.0052
## [433,]   -0.01019616745   0.89556046       0.0000      0.00000 0.0040
## [434,]    0.06168882601   2.23891896       0.0000      0.00000 0.0040
## [435,]    0.01424787648   1.20605711       0.0000      0.00000 0.0044
## [436,]    0.13148860227   2.86951777       0.0000      0.00000 0.0048
## [437,]   -0.04200287073   1.46199400       0.0000      0.00000 0.0056
## [438,]    0.03549627416   1.53971013       0.0000      0.00000 0.0032
## [439,]    0.00254174268   0.51650997       0.0000      0.00000 0.0020
## [440,]   -0.03717111308   1.08311480       0.0000      0.00000 0.0032
## [441,]   -0.04277335864   1.18410415       0.0000      0.00000 0.0032
## [442,]    0.00149190949   0.20418528       0.0000      0.00000 0.0028
## [443,]   -0.03724518831   0.93390795       0.0000      0.00000 0.0048
## [444,]    0.00950819891   0.27832736       0.0000      0.00000 0.0016
## [445,]   -0.07467692227   1.12492898       0.0000      0.00000 0.0080
## [446,]   -0.02675256537   0.62651854       0.0000      0.00000 0.0032
## [447,]    0.00209474836   0.45206789       0.0000      0.00000 0.0032
## [448,]    0.00157181417   0.44878424       0.0000      0.00000 0.0036
## [449,]    0.06728262930   2.37611043       0.0000      0.00000 0.0048
## [450,]   -0.00166880028   1.18391441       0.0000      0.00000 0.0024
## [451,]    0.04919560794   2.37295036       0.0000      0.00000 0.0040
## [452,]    0.02867563482   1.33434716       0.0000      0.00000 0.0052
## [453,]    0.01178068497   0.61822085       0.0000      0.00000 0.0032
## [454,]   -0.00130181320   0.14426606       0.0000      0.00000 0.0020
## [455,]    0.04048774527   2.00171838       0.0000      0.00000 0.0028
## [456,]    0.09654335953   3.28745380       0.0000      0.00000 0.0064
## [457,]   -0.00681667533   0.21921116       0.0000      0.00000 0.0028
## [458,]   -0.00884216914   1.48224398       0.0000      0.00000 0.0044
## [459,]    0.00104958090   0.30917164       0.0000      0.00000 0.0032
## [460,]   -0.00456356564   0.39301482       0.0000      0.00000 0.0052
## [461,]    0.06564913935   2.42610899       0.0000      0.00000 0.0028
## [462,]   -0.01477007871   0.57898870       0.0000      0.00000 0.0032
## [463,]   -0.01798170440   0.68926394       0.0000      0.00000 0.0040
## [464,]    0.02493077960   1.46593060       0.0000      0.00000 0.0020
## [465,]    0.00427014686   0.65096612       0.0000      0.00000 0.0044
## [466,]   -0.04586435621   3.02225301       0.0000      0.00000 0.0048
## [467,]    0.00823242359   0.92196690       0.0000      0.00000 0.0040
## [468,]   -0.00263699252   0.33951782       0.0000      0.00000 0.0028
## [469,]   -0.01636722712   0.57053464       0.0000      0.00000 0.0036
## [470,]    0.06217040766   1.84547466       0.0000      0.00000 0.0060
## [471,]    0.00105138293   0.48743575       0.0000      0.00000 0.0036
## [472,]    0.01670018884   0.64124993       0.0000      0.00000 0.0036
## [473,]   -0.01928640158   0.52752192       0.0000      0.00000 0.0032
## [474,]   -0.00049228771   0.30890649       0.0000      0.00000 0.0032
## [475,]    0.00240431957   0.22468582       0.0000      0.00000 0.0012
## [476,]    0.00920124609   0.34806133       0.0000      0.00000 0.0032
## [477,]   -0.00743187635   0.43327958       0.0000      0.00000 0.0044
## [478,]   -0.05693463230   2.84648834       0.0000      0.00000 0.0032
## [479,]    0.00800172854   0.99425156       0.0000      0.00000 0.0036
## [480,]   -0.01946916718   1.00082842       0.0000      0.00000 0.0052
## [481,]   -1.76355429868  18.76659362       0.0000      0.00000 0.0128
## [482,]   -0.05171996027   1.33527983       0.0000      0.00000 0.0044
## [483,]   -0.00204536825   0.38605785       0.0000      0.00000 0.0024
## [484,]   -0.00661111559   0.24393115       0.0000      0.00000 0.0036
## [485,]   -0.03790171775   0.81395624       0.0000      0.00000 0.0044
## [486,]    0.05874173209   2.17134495       0.0000      0.00000 0.0028
## [487,]    0.00882558811   1.15201195       0.0000      0.00000 0.0032
## [488,]    0.09373968335   2.38740002       0.0000      0.00000 0.0044
## [489,]   -0.24265656950   5.41422863       0.0000      0.00000 0.0076
## [490,]   -0.00297522344   0.38129810       0.0000      0.00000 0.0040
## [491,]   -0.01405131928   0.32906407       0.0000      0.00000 0.0028
## [492,]   -0.11643796358   4.23479183       0.0000      0.00000 0.0016
## [493,]   -0.07660239145   3.04746788       0.0000      0.00000 0.0040
## [494,]   -0.02467583671   0.48242541       0.0000      0.00000 0.0052
## [495,]   -0.01505241630   0.57521722       0.0000      0.00000 0.0060
## [496,]    0.00472762758   0.32939611       0.0000      0.00000 0.0024
## [497,]    0.00966789029   0.51551760       0.0000      0.00000 0.0020
## [498,]    0.00725764033   0.27281656       0.0000      0.00000 0.0024
## [499,]   -0.02566659570   0.84877953       0.0000      0.00000 0.0048
## [500,]    0.00851954413   0.41439800       0.0000      0.00000 0.0028
## [501,]   -0.03617377259   1.09885199       0.0000      0.00000 0.0084
## [502,]   -0.00219021991   0.33797376       0.0000      0.00000 0.0048
## [503,]   -0.02571104412   0.59598753       0.0000      0.00000 0.0044
## [504,]   -0.01308767791   1.91164244       0.0000      0.00000 0.0036
## [505,]   -0.00598417314   0.37484637       0.0000      0.00000 0.0044
## [506,]   -0.00024924542   0.29327741       0.0000      0.00000 0.0024
## [507,]   -0.43711346285   7.97339602       0.0000      0.00000 0.0092
## [508,]   -0.01614102783   0.43188580       0.0000      0.00000 0.0020
## [509,]   -0.00554265436   0.93327980       0.0000      0.00000 0.0028
## [510,]    0.00848278068   0.36633751       0.0000      0.00000 0.0020
## [511,]   -0.00744318163   0.30076754       0.0000      0.00000 0.0036
## [512,]   -0.00131127310   0.11834656       0.0000      0.00000 0.0016
## [513,]   -0.01770089669   0.76265633       0.0000      0.00000 0.0028
## [514,]    0.06786850097   1.90693419       0.0000      0.00000 0.0040
## [515,]   -1.23770861644  12.16867833       0.0000      0.00000 0.0136
## [516,]   -0.02113080011   0.71308653       0.0000      0.00000 0.0036
## [517,]   -0.01072219931   0.20518974       0.0000      0.00000 0.0032
## [518,]    0.03178164808   2.44023339       0.0000      0.00000 0.0040
## [519,]   -0.01684885767   0.77648843       0.0000      0.00000 0.0040
## [520,]   -0.00275489532   0.49283126       0.0000      0.00000 0.0032
## [521,]   -0.00487853912   0.14948587       0.0000      0.00000 0.0024
## [522,]   -0.00689248391   0.21482224       0.0000      0.00000 0.0028
## [523,]    0.00060057733   0.28176150       0.0000      0.00000 0.0032
## [524,]   -0.02085381465   0.49530705       0.0000      0.00000 0.0044
## [525,]    0.00138143637   0.41482678       0.0000      0.00000 0.0036
## [526,]    0.00035632524   0.20395211       0.0000      0.00000 0.0024
## [527,]   -0.11477911361   3.57718129       0.0000      0.00000 0.0040
## [528,]   -0.12262856312   3.36962830       0.0000      0.00000 0.0056
## [529,]   -0.11530666321   3.97492543       0.0000      0.00000 0.0024
## [530,]   -0.00275144915   0.75625991       0.0000      0.00000 0.0040
## [531,]   -0.00735619946   0.37903792       0.0000      0.00000 0.0040
## [532,]   -0.02816282529   0.97582226       0.0000      0.00000 0.0024
## [533,]   -0.18852465895   6.33422859       0.0000      0.00000 0.0056
## [534,]    0.04271752291   1.59850764       0.0000      0.00000 0.0036
## [535,]    0.00546248646   0.73140857       0.0000      0.00000 0.0064
## [536,]   -0.07526001474   2.77114629       0.0000      0.00000 0.0040
## [537,]    0.04842987587   2.15711765       0.0000      0.00000 0.0044
## [538,]   -0.10531864019   2.75819050       0.0000      0.00000 0.0052
## [539,]   -0.09122011903   3.35642205       0.0000      0.00000 0.0068
## [540,]   -0.07392867207   1.80851589       0.0000      0.00000 0.0060
## [541,]    0.73728768737   8.35656650       0.0000      0.00000 0.0104
## [542,]   -0.01422977451   0.42053700       0.0000      0.00000 0.0032
## [543,]    0.00008822763   0.18198245       0.0000      0.00000 0.0020
## [544,]   -0.05600024284   2.67887897       0.0000      0.00000 0.0060
## [545,]   -0.01675438807   0.86876282       0.0000      0.00000 0.0032
## [546,]   -0.01844651235   0.85495534       0.0000      0.00000 0.0044
## [547,]    0.00067229922   0.24343816       0.0000      0.00000 0.0024
## [548,]   -0.00991587718   0.91552641       0.0000      0.00000 0.0040
## [549,]   -0.03331162431   0.86764105       0.0000      0.00000 0.0048
## [550,]   -0.00505001268   0.87023075       0.0000      0.00000 0.0048
## [551,]   -0.01079844118   0.38826517       0.0000      0.00000 0.0040
## [552,]   -0.02468132170   0.37636717       0.0000      0.00000 0.0056
## [553,]   -0.01076864881   0.52380260       0.0000      0.00000 0.0032
## [554,]   -0.12346642412   4.14227539       0.0000      0.00000 0.0040
## [555,]   -0.03197969124   1.06715308       0.0000      0.00000 0.0016
## [556,]   -0.01613152375   0.34459701       0.0000      0.00000 0.0036
## [557,]    0.02369512101   1.57161996       0.0000      0.00000 0.0032
## [558,]   -0.21644343498   4.51840559       0.0000      0.00000 0.0048
## [559,]   -2.52120357785  21.06298272       0.0000      0.00000 0.0156
## [560,]    0.00450279799   0.81418359       0.0000      0.00000 0.0036
## [561,]   -0.07534577830   2.24637916       0.0000      0.00000 0.0044
## [562,]   -0.00081058325   0.17835876       0.0000      0.00000 0.0028
## [563,]   -0.01844337416   0.44325600       0.0000      0.00000 0.0052
## [564,]   -0.00855050408   0.61149625       0.0000      0.00000 0.0020
## [565,]   -0.39840645592   7.15214717       0.0000      0.00000 0.0084
## [566,]   -0.01807388709   0.58641112       0.0000      0.00000 0.0044
## [567,]    0.12368804961   3.07356220       0.0000      0.00000 0.0056
## [568,]   -0.00683178012   0.26863284       0.0000      0.00000 0.0024
## [569,]    0.00521375427   0.37131644       0.0000      0.00000 0.0044
## [570,]   -0.23051694507   5.59947672       0.0000      0.00000 0.0048
## [571,]   -0.00054614480   0.36254194       0.0000      0.00000 0.0016
## [572,]   -0.00819245478   0.58288942       0.0000      0.00000 0.0032
## [573,]   -0.01020156786   0.34905642       0.0000      0.00000 0.0032
## [574,]   -0.03265440546   0.91909646       0.0000      0.00000 0.0032
## [575,]   -0.00350038078   0.19468856       0.0000      0.00000 0.0020
## [576,]   -0.02611565392   0.73899424       0.0000      0.00000 0.0052
## [577,]   -0.01080045463   0.27339202       0.0000      0.00000 0.0024
## [578,]    0.02512100916   1.00045512       0.0000      0.00000 0.0024
## [579,]   -0.06767856462   2.59752948       0.0000      0.00000 0.0052
## [580,]   -0.03329558847   0.71294721       0.0000      0.00000 0.0048
## [581,]   -0.06782222313   2.18598228       0.0000      0.00000 0.0040
## [582,]    0.03083758922   1.32464627       0.0000      0.00000 0.0044
## [583,]   -0.03395567609   0.65947013       0.0000      0.00000 0.0056
## [584,]   -0.03427454161   0.96079148       0.0000      0.00000 0.0044
## [585,]   -6.16978249679  33.31088242    -152.1335      0.00000 0.0372
## [586,]    0.00085359015   0.44504132       0.0000      0.00000 0.0016
## [587,]    0.01486566609   1.02490590       0.0000      0.00000 0.0012
## [588,]    0.00851374278   0.96942383       0.0000      0.00000 0.0024
## [589,]   -0.00470751235   0.14975575       0.0000      0.00000 0.0016
## [590,]   -0.09961813867   3.02783982       0.0000      0.00000 0.0064
## [591,]   -0.00463027725   1.16905344       0.0000      0.00000 0.0028
## [592,]   -0.19654397812   4.07820515       0.0000      0.00000 0.0076
## [593,]    0.06048753379   2.06430420       0.0000      0.00000 0.0040
## [594,]   -0.02042001292   0.59591622       0.0000      0.00000 0.0036
## [595,]   -0.01097424571   0.36067710       0.0000      0.00000 0.0040
## [596,]   -0.33842952675   7.28722973       0.0000      0.00000 0.0048
## [597,]   -0.01722871641   0.31106051       0.0000      0.00000 0.0040
## [598,]   -0.04177102648   1.19046977       0.0000      0.00000 0.0040
## [599,]   -0.01531378583   0.85921816       0.0000      0.00000 0.0056
## [600,]   -0.02557765721   0.89434985       0.0000      0.00000 0.0040
## [601,]    0.01680037778   0.93988523       0.0000      0.00000 0.0048
## [602,]   -0.00641306660   0.40721418       0.0000      0.00000 0.0028
## [603,]   -0.00993149028   0.97391909       0.0000      0.00000 0.0032
## [604,]   -0.02368567356   0.51359946       0.0000      0.00000 0.0036
## [605,]   -0.08306010525   3.15728566       0.0000      0.00000 0.0048
## [606,]   -0.08701214251   3.54668836       0.0000      0.00000 0.0044
## [607,]    0.03408322299   2.08952751       0.0000      0.00000 0.0032
## [608,]   -0.01329750285   0.43319378       0.0000      0.00000 0.0032
## [609,]   -0.01021620899   0.44545648       0.0000      0.00000 0.0020
## [610,]   -0.00402057825   0.34884581       0.0000      0.00000 0.0036
## [611,]   -6.25150205380  35.05747568    -150.8366      0.00000 0.0376
## [612,]   -0.05714263993   2.53987852       0.0000      0.00000 0.0044
## [613,]   -0.01991663835   0.53208681       0.0000      0.00000 0.0032
## [614,]   -0.03218749055   0.92018609       0.0000      0.00000 0.0044
## [615,]   -0.01078061418   0.35453541       0.0000      0.00000 0.0024
## [616,]   -0.06686510156   3.03215726       0.0000      0.00000 0.0044
## [617,]   -0.08743866217   2.32477229       0.0000      0.00000 0.0044
## [618,]    0.00047815682   0.45384720       0.0000      0.00000 0.0028
## [619,]   -0.00918848752   3.12442231       0.0000      0.00000 0.0040
## [620,]   -0.01625386930   0.56441447       0.0000      0.00000 0.0032
## [621,]   -0.00573109037   0.24509410       0.0000      0.00000 0.0024
## [622,]   -0.01294254831   0.48673378       0.0000      0.00000 0.0040
## [623,]   -0.02708931699   0.76391502       0.0000      0.00000 0.0040
## [624,]   -0.02406197135   0.99854251       0.0000      0.00000 0.0040
## [625,]   -0.01566806883   0.30471912       0.0000      0.00000 0.0036
## [626,]   -0.03455858921   0.79688611       0.0000      0.00000 0.0052
## [627,]   -0.00212352621   0.16309414       0.0000      0.00000 0.0020
## [628,]   -0.01412263110   0.50636490       0.0000      0.00000 0.0024
## [629,]   -0.01529110367   0.43610679       0.0000      0.00000 0.0036
## [630,]   -0.02385720566   1.02470392       0.0000      0.00000 0.0036
## [631,]    0.00035956568   0.32055241       0.0000      0.00000 0.0032
## [632,]    0.00630822645   0.71775118       0.0000      0.00000 0.0044
## [633,]   -0.01258286804   0.45436808       0.0000      0.00000 0.0056
## [634,]   -0.01884301231   0.52812447       0.0000      0.00000 0.0056
## [635,]    0.01313285612   1.06463630       0.0000      0.00000 0.0028
## [636,]   -0.01917986290   0.89084126       0.0000      0.00000 0.0024
## [637,]   -0.06538068084   3.08183618       0.0000      0.00000 0.0052
## [638,]   -0.00734308067   0.29547006       0.0000      0.00000 0.0040
## [639,]   -0.01664597928   0.50535990       0.0000      0.00000 0.0060
## [640,]   -0.02634663289   0.56193027       0.0000      0.00000 0.0048
## [641,]   -0.00905324719   0.42045398       0.0000      0.00000 0.0052
## [642,]   -0.00846997663   0.74586804       0.0000      0.00000 0.0032
## [643,]   -0.00697977824   0.33210343       0.0000      0.00000 0.0028
## [644,]   -0.19601449582   5.07965513       0.0000      0.00000 0.0048
## [645,]   -0.00165916235   0.32875539       0.0000      0.00000 0.0048
## [646,]   -0.27687138686   5.56706303       0.0000      0.00000 0.0080
## [647,]   -0.00790607460   0.21719232       0.0000      0.00000 0.0024
## [648,]    0.00220809274   0.55195592       0.0000      0.00000 0.0040
## [649,]    0.00486925544   0.34839125       0.0000      0.00000 0.0036
## [650,]   -0.00462845550   0.32010838       0.0000      0.00000 0.0020
## [651,]   -0.00521275018   0.16915243       0.0000      0.00000 0.0020
## [652,]   -0.03140453282   0.93119953       0.0000      0.00000 0.0028
## [653,]    0.00381181407   0.21260252       0.0000      0.00000 0.0008
## [654,]   -0.02592653809   0.59060945       0.0000      0.00000 0.0044
## [655,]   -0.01811238025   0.66997062       0.0000      0.00000 0.0036
## [656,]   -0.01019049691   0.39956909       0.0000      0.00000 0.0028
## [657,]    0.01579965009   1.31401020       0.0000      0.00000 0.0040
## [658,]   -0.10741662597   4.37757491       0.0000      0.00000 0.0040
## [659,]   -0.12020088607   3.69001858       0.0000      0.00000 0.0024
## [660,]   -0.00529449306   0.25263108       0.0000      0.00000 0.0032
## [661,]   -0.03623419293   1.23218225       0.0000      0.00000 0.0028
## [662,]   -0.80304827285  10.31142488       0.0000      0.00000 0.0084
## [663,]   -0.36665734707   6.96915918       0.0000      0.00000 0.0072
## [664,]    0.00089479405   0.60153488       0.0000      0.00000 0.0032
## [665,]    0.00318168175   0.50027252       0.0000      0.00000 0.0028
## [666,]   -0.02178480035   0.58246623       0.0000      0.00000 0.0044
## [667,]   -0.00798472201   0.35787986       0.0000      0.00000 0.0016
## [668,]   -0.18045180228   3.63743561       0.0000      0.00000 0.0064
## [669,]    0.00690934886   0.45148791       0.0000      0.00000 0.0032
## [670,]   -0.15319054144   2.53403193       0.0000      0.00000 0.0072
## [671,]   -0.02385689138   0.88873503       0.0000      0.00000 0.0020
## [672,]   -0.01374904597   0.52279597       0.0000      0.00000 0.0028
## [673,]   -0.00575106273   0.39720587       0.0000      0.00000 0.0048
## [674,]   -0.29458109077   5.86194441       0.0000      0.00000 0.0064
## [675,]   -0.04503259346   0.87201354       0.0000      0.00000 0.0044
## [676,]   -0.00542199546   0.27467683       0.0000      0.00000 0.0016
## [677,]   -0.01067440578   0.25157526       0.0000      0.00000 0.0024
## [678,]   -0.27525068086   4.72668606       0.0000      0.00000 0.0072
## [679,]   -0.00152820187   0.27963285       0.0000      0.00000 0.0020
## [680,]   -0.06602514049   1.70130620       0.0000      0.00000 0.0056
## [681,]    0.02908860103   1.08433178       0.0000      0.00000 0.0016
## [682,]    0.01689078693   1.46996297       0.0000      0.00000 0.0032
## [683,]   -0.00581012623   0.25055465       0.0000      0.00000 0.0032
## [684,]   -0.02021446488   0.46104437       0.0000      0.00000 0.0044
## [685,]   -0.07116631254   2.35218504       0.0000      0.00000 0.0048
## [686,]   -0.02720137318   0.95292982       0.0000      0.00000 0.0052
## [687,]   -0.01667264217   0.51533834       0.0000      0.00000 0.0040
## [688,]   -0.01919501060   0.84899793       0.0000      0.00000 0.0044
## [689,]   -0.61029405909   9.59225940       0.0000      0.00000 0.0076
## [690,]   -0.07287090867   1.89400144       0.0000      0.00000 0.0048
## [691,]    0.03117001282   1.75713325       0.0000      0.00000 0.0016
## [692,]   -0.09945375428   2.51140400       0.0000      0.00000 0.0048
## [693,]   -0.01487130862   0.50732573       0.0000      0.00000 0.0040
## [694,]    0.02016369622   1.48900965       0.0000      0.00000 0.0024
## [695,]    0.07853813440   2.87095205       0.0000      0.00000 0.0056
## [696,]   -0.07986366102   2.91589908       0.0000      0.00000 0.0064
## [697,]    0.08490171280   2.64061809       0.0000      0.00000 0.0036
## [698,]   -0.05899234853   2.16326746       0.0000      0.00000 0.0036
## [699,]   -0.00329126955   0.23356264       0.0000      0.00000 0.0020
## [700,]   -0.27534672630   6.56685696       0.0000      0.00000 0.0052
## [701,]   -0.00806030018   0.34443363       0.0000      0.00000 0.0028
## [702,]   -0.01013860162   0.78816363       0.0000      0.00000 0.0040
## [703,]   -0.02143911209   0.44654366       0.0000      0.00000 0.0040
## [704,]   -0.02669023315   0.77350618       0.0000      0.00000 0.0040
## [705,]    0.04141267459   1.54081181       0.0000      0.00000 0.0032
## [706,]    0.00226294831   0.35445201       0.0000      0.00000 0.0044
## [707,]   -0.03303268348   0.84476512       0.0000      0.00000 0.0048
## [708,]   -0.01160823315   0.56099623       0.0000      0.00000 0.0040
## [709,]   -0.00635494262   0.35944750       0.0000      0.00000 0.0036
## [710,]    0.04520069231   3.30998920       0.0000      0.00000 0.0052
## [711,]   -0.01777173315   0.68990287       0.0000      0.00000 0.0024
## [712,]   -0.02189853965   0.60907811       0.0000      0.00000 0.0032
## [713,]   -0.03278246162   1.08868488       0.0000      0.00000 0.0040
## [714,]   -0.04646872397   1.37795145       0.0000      0.00000 0.0044
## [715,]   -0.97633663142  12.13436899       0.0000      0.00000 0.0096
## [716,]    0.00041403376   0.96440102       0.0000      0.00000 0.0040
## [717,]   -0.00243589264   0.55716014       0.0000      0.00000 0.0028
## [718,]   -0.03140013911   0.62951857       0.0000      0.00000 0.0032
## [719,]   -0.02553283917   0.62318065       0.0000      0.00000 0.0032
## [720,]   -0.05622686401   1.71438085       0.0000      0.00000 0.0052
## [721,]   -0.01284337506   1.84060116       0.0000      0.00000 0.0052
## [722,]   -0.02769424852   0.76660660       0.0000      0.00000 0.0040
## [723,]    0.47022087004   6.59906072       0.0000      0.00000 0.0092
## [724,]   -0.01109527792   0.62473872       0.0000      0.00000 0.0028
## [725,]   -0.01635231371   0.51039839       0.0000      0.00000 0.0048
## [726,]   -0.01575908862   0.79925866       0.0000      0.00000 0.0044
## [727,]   -0.00706276861   0.20749028       0.0000      0.00000 0.0028
## [728,]   -0.03442170712   0.71864012       0.0000      0.00000 0.0044
## [729,]   -0.01996918928   0.63925587       0.0000      0.00000 0.0048
## [730,]   -0.06906748911   1.80453514       0.0000      0.00000 0.0052
## [731,]   -0.00812970724   0.42756813       0.0000      0.00000 0.0044
## [732,]   -0.03990865497   1.01934928       0.0000      0.00000 0.0028
## [733,]   -0.01613020637   0.64276676       0.0000      0.00000 0.0044
## [734,]    0.00463493246   0.57770717       0.0000      0.00000 0.0020
## [735,]    0.05425932404   2.52405836       0.0000      0.00000 0.0028
## [736,]   -0.02137925793   1.27743333       0.0000      0.00000 0.0032
## [737,]   -0.11636730244   4.25156934       0.0000      0.00000 0.0052
## [738,]   -0.00933582507   0.36424341       0.0000      0.00000 0.0048
## [739,]   -0.01689753800   0.38393045       0.0000      0.00000 0.0032
## [740,]   -0.01496408271   0.27598012       0.0000      0.00000 0.0040
## [741,]    0.01212822901   3.99332700       0.0000      0.00000 0.0044
## [742,]    0.01414875155   0.87022017       0.0000      0.00000 0.0036
## [743,]   -0.01892256195   0.63632012       0.0000      0.00000 0.0016
## [744,]   -0.01759978179   1.08441120       0.0000      0.00000 0.0040
## [745,]    0.03557865145   1.35222242       0.0000      0.00000 0.0044
## [746,]   -0.04372623547   1.04865325       0.0000      0.00000 0.0048
## [747,]    0.02213702164   1.68815240       0.0000      0.00000 0.0040
## [748,]   -0.94371972114  11.14448282       0.0000      0.00000 0.0112
## [749,]    1.79459201349  13.85952633       0.0000      0.00000 0.0212
## [750,]   -0.02946964620   0.82575788       0.0000      0.00000 0.0036
## [751,]    0.00177158701   0.27312243       0.0000      0.00000 0.0044
## [752,]   -0.08542823113   3.20990084       0.0000      0.00000 0.0020
## [753,]   -0.00777424026   0.48163682       0.0000      0.00000 0.0032
## [754,]   -0.01135251454   0.35147502       0.0000      0.00000 0.0040
## [755,]    0.00229807127   0.13340158       0.0000      0.00000 0.0016
## [756,]   -0.00435365163   0.11300572       0.0000      0.00000 0.0024

4.3.4 Predict fitted values for each individual

pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals

4.3.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")

4.4 Fit the NPB model without ozone and with temperature

Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone but with temperature just to see if something else pops up instead.

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
# fit.npb3 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2)], Y = Y, W = W.scaled2,
#                 scaleY = TRUE,
#                 priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb3, file = here::here("Results", "NPB_Birth_Weight_v4.3.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4.3.rdata"))
npb.sum3 <- summary(fit.npb3)

4.4.1 First, main effect regression coefficients with PIPs

rownames(npb.sum3$main.effects) <- colnames(X.scaled[,-c(2)])
npb.sum3$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                 -5.0812657 11.389288   -38.420777     4.123733 0.4308
## mean_temp               -4.3626863 13.839561   -38.100412     7.899612 0.4064
## pct_tree_cover          -1.0942565  5.378364   -14.926393     8.862679 0.2992
## pct_impervious          -1.6628395  5.689727   -17.895070     5.520513 0.3044
## mean_aadt_intensity     -0.1461904  5.585696   -10.742507    12.956853 0.2856
## dist_m_tri              -1.0196214  5.847048   -15.541244    10.630242 0.3096
## dist_m_npl              -0.5963490  4.986723   -12.544201    10.099711 0.2736
## dist_m_waste_site        1.7286714  9.421148    -9.610017    32.957196 0.3028
## dist_m_major_emit        0.3675718  6.164625    -9.898133    15.820179 0.2704
## dist_m_cafo             -1.9038253 12.951734   -26.013467    12.491398 0.3528
## dist_m_mine_well        -3.4827117  9.222471   -31.808167     6.997606 0.3928
## cvd_rate_adj            -2.1767251  6.695723   -21.070834     5.664834 0.3408
## res_rate_adj            -3.1881258  8.110302   -28.146459     3.997973 0.3732
## violent_crime_rate      -0.5876895  6.508686   -14.093171    11.614945 0.2952
## property_crime_rate     -2.0397891  6.325035   -21.728442     5.620994 0.3164
## pct_less_hs             -1.8967882  7.213950   -22.183937     7.013704 0.3464
## pct_unemp               -5.8335999 12.030417   -44.665861     1.948495 0.4236
## pct_limited_eng         -1.5263159  5.896443   -18.006636     5.145165 0.3028
## pct_hh_pov              -1.0088890  5.682389   -13.882495     8.026244 0.2944
## pct_poc                 -1.2612110  6.168611   -15.669226     8.062277 0.3088

4.4.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum3$interactions
##           Posterior Mean           SD 95% CI Lower 95% CI Upper    PIP
##   [1,]   -0.002769623604  0.198664905       0.0000       0.0000 0.0012
##   [2,]    0.002676103140  0.226259859       0.0000       0.0000 0.0008
##   [3,]   -0.017689095548  0.454321419       0.0000       0.0000 0.0016
##   [4,]    0.022607066757  0.706450372       0.0000       0.0000 0.0016
##   [5,]   -0.004815508237  0.454880039       0.0000       0.0000 0.0008
##   [6,]   -0.003618262125  0.207005072       0.0000       0.0000 0.0012
##   [7,]   -0.010175297406  0.470189316       0.0000       0.0000 0.0024
##   [8,]   -0.006493587924  0.246554838       0.0000       0.0000 0.0016
##   [9,]   -0.010169208510  0.324262064       0.0000       0.0000 0.0012
##  [10,]   -0.006256413501  0.216784895       0.0000       0.0000 0.0016
##  [11,]    0.000075906071  0.254461017       0.0000       0.0000 0.0016
##  [12,]   -0.002315005571  0.115750279       0.0000       0.0000 0.0004
##  [13,]   -0.001431785327  0.315273728       0.0000       0.0000 0.0024
##  [14,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
##  [15,]    0.000207662552  0.010383128       0.0000       0.0000 0.0004
##  [16,]   -0.002920286744  0.146014337       0.0000       0.0000 0.0004
##  [17,]   -0.005366736115  0.268336806       0.0000       0.0000 0.0004
##  [18,]   -0.019314605808  0.604048841       0.0000       0.0000 0.0016
##  [19,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
##  [20,]   -0.014699578938  0.403945782       0.0000       0.0000 0.0020
##  [21,]    0.002207182138  0.328897169       0.0000       0.0000 0.0016
##  [22,]   -0.012640978532  0.439895464       0.0000       0.0000 0.0012
##  [23,]   -0.037838205015  0.801984518       0.0000       0.0000 0.0032
##  [24,]   -0.002452025727  0.231625135       0.0000       0.0000 0.0012
##  [25,]   -0.006340093628  0.306499632       0.0000       0.0000 0.0012
##  [26,]   -0.003825092245  0.537817746       0.0000       0.0000 0.0012
##  [27,]   -0.028016195737  0.835301220       0.0000       0.0000 0.0024
##  [28,]   -0.006770226758  0.259096849       0.0000       0.0000 0.0008
##  [29,]   -0.005833794573  0.195134526       0.0000       0.0000 0.0012
##  [30,]   -0.003382051342  0.172974543       0.0000       0.0000 0.0008
##  [31,]   -0.019817398383  0.667056390       0.0000       0.0000 0.0012
##  [32,]   -0.000485441096  0.024272055       0.0000       0.0000 0.0004
##  [33,]    0.002785191465  0.152715661       0.0000       0.0000 0.0016
##  [34,]    0.002619637285  0.364446135       0.0000       0.0000 0.0016
##  [35,]    0.002892476028  0.338203520       0.0000       0.0000 0.0016
##  [36,]    0.004819809569  0.273732352       0.0000       0.0000 0.0012
##  [37,]    0.002825693695  0.314887061       0.0000       0.0000 0.0012
##  [38,]    0.000648084403  0.032404220       0.0000       0.0000 0.0004
##  [39,]    0.004200631152  0.359057907       0.0000       0.0000 0.0008
##  [40,]   -0.002348263080  0.134685014       0.0000       0.0000 0.0012
##  [41,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
##  [42,]   -0.007539389382  0.245251653       0.0000       0.0000 0.0024
##  [43,]    0.030311034884  1.000450173       0.0000       0.0000 0.0012
##  [44,]   -0.001030528481  0.150591214       0.0000       0.0000 0.0008
##  [45,]   -0.009494168271  0.393523172       0.0000       0.0000 0.0008
##  [46,]    0.000450137268  0.384231330       0.0000       0.0000 0.0012
##  [47,]   -0.008536496303  0.435130695       0.0000       0.0000 0.0016
##  [48,]   -0.013952811051  0.450805324       0.0000       0.0000 0.0020
##  [49,]   -0.003586128585  0.138081806       0.0000       0.0000 0.0008
##  [50,]   -0.008938348458  0.311250524       0.0000       0.0000 0.0020
##  [51,]   -0.006595719891  0.202351834       0.0000       0.0000 0.0016
##  [52,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
##  [53,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
##  [54,]   -0.023124765682  0.711427982       0.0000       0.0000 0.0020
##  [55,]    0.004256201627  0.376006383       0.0000       0.0000 0.0024
##  [56,]   -0.000086827426  0.238246181       0.0000       0.0000 0.0020
##  [57,]    0.000422048717  0.021102436       0.0000       0.0000 0.0004
##  [58,]   -0.000196335845  0.009816792       0.0000       0.0000 0.0004
##  [59,]   -0.000939553726  0.046977686       0.0000       0.0000 0.0004
##  [60,]   -0.008883954457  0.314042246       0.0000       0.0000 0.0008
##  [61,]    0.005385011084  0.269250554       0.0000       0.0000 0.0004
##  [62,]   -0.050241440971  1.077723283       0.0000       0.0000 0.0032
##  [63,]   -0.002271831586  0.155904862       0.0000       0.0000 0.0012
##  [64,]   -0.004324079959  0.158515992       0.0000       0.0000 0.0008
##  [65,]   -0.005549417512  0.196710517       0.0000       0.0000 0.0008
##  [66,]   -0.009435258517  0.413831614       0.0000       0.0000 0.0008
##  [67,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
##  [68,]   -0.015479638368  0.612589501       0.0000       0.0000 0.0024
##  [69,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
##  [70,]   -0.004799254986  0.239962749       0.0000       0.0000 0.0004
##  [71,]    0.009534850957  0.488029163       0.0000       0.0000 0.0008
##  [72,]   -0.000370767004  0.482264779       0.0000       0.0000 0.0016
##  [73,]    0.004766936626  0.322944110       0.0000       0.0000 0.0020
##  [74,]   -0.004026562566  0.128292250       0.0000       0.0000 0.0012
##  [75,]   -0.008634181121  0.266856544       0.0000       0.0000 0.0012
##  [76,]    0.001172309950  0.109324693       0.0000       0.0000 0.0008
##  [77,]   -0.016923851571  0.406257633       0.0000       0.0000 0.0020
##  [78,]   -0.011278818285  0.305233323       0.0000       0.0000 0.0016
##  [79,]   -0.000346309058  0.017315453       0.0000       0.0000 0.0004
##  [80,]   -0.001816860159  0.153133347       0.0000       0.0000 0.0012
##  [81,]   -0.000332692986  0.035777847       0.0000       0.0000 0.0012
##  [82,]   -0.001153712032  0.194481961       0.0000       0.0000 0.0012
##  [83,]    0.006479901384  0.329735569       0.0000       0.0000 0.0016
##  [84,]   -0.003525837893  0.176291895       0.0000       0.0000 0.0004
##  [85,]    0.001482732895  0.074136645       0.0000       0.0000 0.0004
##  [86,]   -0.000184188273  0.141252786       0.0000       0.0000 0.0012
##  [87,]   -0.019799396816  0.471855326       0.0000       0.0000 0.0024
##  [88,]   -0.002581285458  0.129064273       0.0000       0.0000 0.0004
##  [89,]    0.015168041767  0.607127084       0.0000       0.0000 0.0008
##  [90,]   -0.003102298889  0.138876258       0.0000       0.0000 0.0008
##  [91,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
##  [92,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
##  [93,]   -0.000008795636  0.107994574       0.0000       0.0000 0.0012
##  [94,]    0.002038018593  0.101900930       0.0000       0.0000 0.0004
##  [95,]    0.007006684774  0.350334239       0.0000       0.0000 0.0004
##  [96,]    0.037361275159  1.135884099       0.0000       0.0000 0.0020
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##  [98,]    0.017830386830  0.628403460       0.0000       0.0000 0.0012
##  [99,]    0.001209729270  0.060486463       0.0000       0.0000 0.0004
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## [113,]    0.015681499999  0.596051699       0.0000       0.0000 0.0008
## [114,]    0.035064629658  1.079114174       0.0000       0.0000 0.0020
## [115,]    0.006580978151  0.298818905       0.0000       0.0000 0.0012
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## [135,]   -0.004323417544  0.270651343       0.0000       0.0000 0.0012
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## [152,]    0.179446648678  3.195583149       0.0000       0.0000 0.0040
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## [168,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
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## [170,]    0.000207662552  0.010383128       0.0000       0.0000 0.0004
## [171,]   -0.001551703242  0.279566939       0.0000       0.0000 0.0012
## [172,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
## [173,]    0.002906158812  0.775963974       0.0000       0.0000 0.0028
## [174,]   -0.000890214056  0.044510703       0.0000       0.0000 0.0004
## [175,]   -0.003339003168  0.136671138       0.0000       0.0000 0.0012
## [176,]   -0.003998606717  0.328971591       0.0000       0.0000 0.0012
## [177,]   -0.004330203533  0.220373039       0.0000       0.0000 0.0008
## [178,]   -0.001253614333  0.062680717       0.0000       0.0000 0.0004
## [179,]   -0.011678839749  0.466685428       0.0000       0.0000 0.0016
## [180,]   -0.002524114490  0.126205724       0.0000       0.0000 0.0004
## [181,]   -0.005846033303  0.280301878       0.0000       0.0000 0.0012
## [182,]   -0.012132317428  0.323828225       0.0000       0.0000 0.0024
## [183,]    0.008351835061  0.348085910       0.0000       0.0000 0.0016
## [184,]   -0.001442031889  0.200213539       0.0000       0.0000 0.0008
## [185,]   -0.026002439515  0.708186627       0.0000       0.0000 0.0024
## [186,]   -0.002982218741  0.149110937       0.0000       0.0000 0.0004
## [187,]   -0.005688428785  0.265412512       0.0000       0.0000 0.0012
## [188,]    0.000579859949  0.028992997       0.0000       0.0000 0.0004
## [189,]   -0.005766144258  0.288307213       0.0000       0.0000 0.0004
## [190,]   -0.019113094364  0.712166723       0.0000       0.0000 0.0016
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## [192,]   -0.001253614333  0.062680717       0.0000       0.0000 0.0004
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## [194,]   -0.014927921129  0.496644830       0.0000       0.0000 0.0024
## [195,]   -0.017785696629  0.525124514       0.0000       0.0000 0.0024
## [196,]   -0.033234756835  1.196091358       0.0000       0.0000 0.0016
## [197,]    0.000076561597  0.003828080       0.0000       0.0000 0.0004
## [198,]   -0.038361090062  1.273061833       0.0000       0.0000 0.0012
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## [203,]    0.010052458677  0.575210468       0.0000       0.0000 0.0020
## [204,]   -0.004766945365  0.168796575       0.0000       0.0000 0.0008
## [205,]   -0.006948081982  0.483281392       0.0000       0.0000 0.0012
## [206,]   -0.304882380878  4.783341928       0.0000       0.0000 0.0052
## [207,]    0.010097608362  0.315958615       0.0000       0.0000 0.0012
## [208,]    0.001726723869  0.247904652       0.0000       0.0000 0.0012
## [209,]   -0.008181644184  0.409082209       0.0000       0.0000 0.0004
## [210,]   -0.056611616761  1.425614182       0.0000       0.0000 0.0020
## [211,]   -0.002924726545  0.725168644       0.0000       0.0000 0.0020
## [212,]   -0.006025811710  0.215321893       0.0000       0.0000 0.0008
## [213,]    0.005357135782  0.267856789       0.0000       0.0000 0.0004
## [214,]    0.028820583904  0.750864527       0.0000       0.0000 0.0024
## [215,]    0.003862822840  0.172133497       0.0000       0.0000 0.0008
## [216,]   -0.004517897354  0.534734102       0.0000       0.0000 0.0012
## [217,]    0.027718773133  0.719698627       0.0000       0.0000 0.0016
## [218,]   -0.002164202039  0.154634507       0.0000       0.0000 0.0008
## [219,]   -0.007197905792  0.288655602       0.0000       0.0000 0.0016
## [220,]   -0.015127393771  0.533828990       0.0000       0.0000 0.0016
## [221,]    0.018764782151  0.666644323       0.0000       0.0000 0.0016
## [222,]    0.026485855476  1.186368058       0.0000       0.0000 0.0024
## [223,]   -0.057017745241  2.143885322       0.0000       0.0000 0.0020
## [224,]   -0.321835265043  5.767827591       0.0000       0.0000 0.0048
## [225,]   -0.005654670806  0.282733540       0.0000       0.0000 0.0004
## [226,]   -0.002920900915  0.146045046       0.0000       0.0000 0.0004
## [227,]    0.619601160733 12.853264774       0.0000       0.0000 0.0040
## [228,]   -0.073415628261  2.654731910       0.0000       0.0000 0.0016
## [229,]   -0.051668049825  2.340713023       0.0000       0.0000 0.0016
## [230,] -402.489599580349 68.861649356    -532.6115    -265.1587 1.0000
## [231,]   -0.022566050756  0.715704958       0.0000       0.0000 0.0020
## [232,]  305.472946739533 57.161971815     197.6906     418.8627 1.0000
## [233,]   -0.009149223632  0.310139698       0.0000       0.0000 0.0012
## [234,]   -0.017963917105  0.480365087       0.0000       0.0000 0.0020
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## [236,]   -0.009476630936  0.280865486       0.0000       0.0000 0.0012
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## [240,]    0.192605698138  3.116360651       0.0000       0.0000 0.0052
## [241,]    0.005155805132  0.178793201       0.0000       0.0000 0.0012
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## [247,]    0.009449490246  0.475701599       0.0000       0.0000 0.0024
## [248,]    0.021440501744  1.072025087       0.0000       0.0000 0.0004
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## [250,]   -0.061439162058  1.876544470       0.0000       0.0000 0.0036
## [251,]   -0.002002356381  0.132281797       0.0000       0.0000 0.0008
## [252,]   -0.031889092234  1.249305491       0.0000       0.0000 0.0012
## [253,]   -0.009790133762  0.473232939       0.0000       0.0000 0.0016
## [254,]   -0.016628971005  0.533262584       0.0000       0.0000 0.0020
## [255,]   -0.003432633304  0.215219538       0.0000       0.0000 0.0016
## [256,]    0.005208960786  1.096103803       0.0000       0.0000 0.0016
## [257,]   -0.003581049661  0.422243194       0.0000       0.0000 0.0012
## [258,]   -0.000075860625  0.185453469       0.0000       0.0000 0.0012
## [259,]   -0.005417554020  0.294217910       0.0000       0.0000 0.0008
## [260,]    0.026683846531  1.169884197       0.0000       0.0000 0.0008
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## [263,]   -0.010925127815  0.348386521       0.0000       0.0000 0.0012
## [264,]    0.021839623961  0.865542246       0.0000       0.0000 0.0016
## [265,]    0.089165710674  2.947293798       0.0000       0.0000 0.0032
## [266,]   -0.000680144062  0.360269713       0.0000       0.0000 0.0008
## [267,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
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## [274,]   -0.008448305620  0.250557669       0.0000       0.0000 0.0016
## [275,]    0.001395809730  0.586512916       0.0000       0.0000 0.0012
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## [411,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
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## [470,]    0.004431618835  0.221580942       0.0000       0.0000 0.0004
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## [582,]   -0.007162754961  0.259833307       0.0000       0.0000 0.0008
## [583,]   -0.002567198771  0.128359939       0.0000       0.0000 0.0004
## [584,]    0.002140552297  0.107027615       0.0000       0.0000 0.0004
## [585,]    0.010778389206  0.643902760       0.0000       0.0000 0.0016
## [586,]    0.000128606060  0.144161811       0.0000       0.0000 0.0008
## [587,]    0.016061902446  0.560748267       0.0000       0.0000 0.0012
## [588,]   -0.004693903271  0.512530911       0.0000       0.0000 0.0024
## [589,]    0.001333434449  0.417468496       0.0000       0.0000 0.0016
## [590,]   -0.062548182325  2.091603994       0.0000       0.0000 0.0036
## [591,]   -0.019998569160  0.871718769       0.0000       0.0000 0.0036
## [592,]    0.031652084470  1.208417966       0.0000       0.0000 0.0020
## [593,]   -0.006378899683  0.226285189       0.0000       0.0000 0.0008
## [594,]   -0.034077857539  1.328378121       0.0000       0.0000 0.0016
## [595,]   -0.002857908926  0.428325690       0.0000       0.0000 0.0012
## [596,]   -0.038183141584  0.799472103       0.0000       0.0000 0.0028
## [597,]    0.010976644428  0.548832221       0.0000       0.0000 0.0004
## [598,]   -0.036581840960  1.980914573       0.0000       0.0000 0.0012
## [599,]    0.028396085483  1.490583480       0.0000       0.0000 0.0024
## [600,]   -0.062260064420  2.646502009       0.0000       0.0000 0.0008
## [601,]   -0.000151016882  0.118687243       0.0000       0.0000 0.0012
## [602,]    0.004837803143  0.785283115       0.0000       0.0000 0.0024
## [603,]    0.035284665497  1.660615416       0.0000       0.0000 0.0008
## [604,]    0.005687379170  0.423291897       0.0000       0.0000 0.0012
## [605,]    0.012543580437  0.575572802       0.0000       0.0000 0.0016
## [606,]    0.009420136850  0.507495108       0.0000       0.0000 0.0012
## [607,]   -0.002982218741  0.149110937       0.0000       0.0000 0.0004
## [608,]   -0.002571778607  0.131894719       0.0000       0.0000 0.0020
## [609,]   -0.002982218741  0.149110937       0.0000       0.0000 0.0004
## [610,]   -0.003409502457  0.120906938       0.0000       0.0000 0.0008
## [611,]   -0.003291467692  0.371958431       0.0000       0.0000 0.0016
## [612,]    0.000515125527  0.225532548       0.0000       0.0000 0.0008
## [613,]   -0.065173514002  2.647215635       0.0000       0.0000 0.0020
## [614,]   -0.000252365306  0.167593474       0.0000       0.0000 0.0012
## [615,]   -0.004712227272  0.183916301       0.0000       0.0000 0.0008
## [616,]   -0.007876361596  0.450509526       0.0000       0.0000 0.0012
## [617,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
## [618,]   -0.006037938944  0.229103964       0.0000       0.0000 0.0008
## [619,]   -0.005933477540  0.211605547       0.0000       0.0000 0.0012
## [620,]    0.006948649657  0.706477716       0.0000       0.0000 0.0016
## [621,]   -0.007373662268  0.284824657       0.0000       0.0000 0.0012
## [622,]   -0.128083789073  3.707601496       0.0000       0.0000 0.0032
## [623,]   -0.029184237911  0.995126859       0.0000       0.0000 0.0020
## [624,]   -0.063391375218  1.691567379       0.0000       0.0000 0.0032
## [625,]    0.001995402942  0.328097682       0.0000       0.0000 0.0008
## [626,]   -0.011925149294  0.353802899       0.0000       0.0000 0.0016
## [627,]   -0.002456849863  0.197307234       0.0000       0.0000 0.0012
## [628,]   -0.012783874737  1.514527731       0.0000       0.0000 0.0020
## [629,]   -0.034807740268  1.001698625       0.0000       0.0000 0.0020
## [630,]   -0.002666642692  0.168241809       0.0000       0.0000 0.0012
## [631,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
## [632,]   -0.081176587716  2.000216865       0.0000       0.0000 0.0032
## [633,]   -0.011070952005  0.338592533       0.0000       0.0000 0.0012
## [634,]   -0.011358992366  0.479905619       0.0000       0.0000 0.0024
## [635,]   -0.004263359399  0.209652801       0.0000       0.0000 0.0012
## [636,]    0.002105648004  0.428719355       0.0000       0.0000 0.0020
## [637,]   -0.017256040974  0.801850694       0.0000       0.0000 0.0020
## [638,]   -0.008099647451  0.242356246       0.0000       0.0000 0.0012
## [639,]   -0.022516922347  0.941866831       0.0000       0.0000 0.0020
## [640,]   -0.005430692422  0.480274828       0.0000       0.0000 0.0016
## [641,]   -0.001599923391  0.065021754       0.0000       0.0000 0.0008
## [642,]   -0.005306290406  0.188517318       0.0000       0.0000 0.0008
## [643,]   -0.006616600927  0.330830046       0.0000       0.0000 0.0004
## [644,]    0.006615043121  0.303179134       0.0000       0.0000 0.0008
## [645,]   -0.012322193010  0.518641820       0.0000       0.0000 0.0012
## [646,]   -0.006538030447  0.187061449       0.0000       0.0000 0.0016
## [647,]    0.005520128318  0.363010478       0.0000       0.0000 0.0008
## [648,]   -0.015227851631  0.466903004       0.0000       0.0000 0.0016
## [649,]    0.028395625035  1.444266989       0.0000       0.0000 0.0008
## [650,]   -0.042718835626  1.125787316       0.0000       0.0000 0.0020
## [651,]    0.162892456930  3.469162025       0.0000       0.0000 0.0040
## [652,]   -0.000655872685  0.159191479       0.0000       0.0000 0.0016
## [653,]   -0.004906092198  0.295956188       0.0000       0.0000 0.0016
## [654,]   -0.029347964213  1.336092126       0.0000       0.0000 0.0012
## [655,]   -0.009509074531  0.292699455       0.0000       0.0000 0.0012
## [656,]   -0.005166752942  0.466258277       0.0000       0.0000 0.0012
## [657,]   -0.006114190351  0.218730160       0.0000       0.0000 0.0008
## [658,]   -0.022986478062  1.058483007       0.0000       0.0000 0.0024
## [659,]   -0.011764487099  0.449341408       0.0000       0.0000 0.0016
## [660,]   -0.023032464802  0.686177804       0.0000       0.0000 0.0020
## [661,]    0.002466843473  0.287069455       0.0000       0.0000 0.0016
## [662,]    0.000008702562  0.169200856       0.0000       0.0000 0.0012
## [663,]   -0.003415979545  0.221966700       0.0000       0.0000 0.0020
## [664,]    0.023147800001  0.969673792       0.0000       0.0000 0.0016
## [665,]   -0.013242589085  0.638309333       0.0000       0.0000 0.0008
## [666,]    0.000002008863  0.316003899       0.0000       0.0000 0.0020
## [667,]   -0.003834899791  0.143457256       0.0000       0.0000 0.0008
## [668,]   -0.000223093125  0.011154656       0.0000       0.0000 0.0004
## [669,]   -0.050083584311  2.763603187       0.0000       0.0000 0.0012
## [670,]   -0.021807779019  0.528047733       0.0000       0.0000 0.0020
## [671,]   -0.013885269152  0.639313910       0.0000       0.0000 0.0012
## [672,]    0.001847485713  1.731376575       0.0000       0.0000 0.0024
## [673,]   -0.010078820283  0.315505506       0.0000       0.0000 0.0016
## [674,]   -0.010346180338  0.427532359       0.0000       0.0000 0.0016
## [675,]   -0.000959532906  0.297550668       0.0000       0.0000 0.0020
## [676,]   -0.007742644433  0.377518875       0.0000       0.0000 0.0016
## [677,]    0.458147979187  6.849257000       0.0000       0.0000 0.0056
## [678,]   -0.018840079189  0.533092295       0.0000       0.0000 0.0020
## [679,]   -0.002567198771  0.128359939       0.0000       0.0000 0.0004
## [680,]   -0.005148509824  0.448626421       0.0000       0.0000 0.0008
## [681,]   -0.008891793505  0.253808903       0.0000       0.0000 0.0020
## [682,]   -0.000036508456  0.176901169       0.0000       0.0000 0.0012
## [683,]   -0.015118982838  0.755949142       0.0000       0.0000 0.0004
## [684,]   -0.020869835882  0.607293670       0.0000       0.0000 0.0020
## [685,]    0.001141787604  0.359977158       0.0000       0.0000 0.0012
## [686,]   -0.015991858798  0.563425781       0.0000       0.0000 0.0016
## [687,]   -0.000550617721  0.163257863       0.0000       0.0000 0.0008
## [688,]   -0.010146534393  0.342032377       0.0000       0.0000 0.0016
## [689,]   -0.011581824963  0.579091248       0.0000       0.0000 0.0004
## [690,]   -0.022256794441  0.633628698       0.0000       0.0000 0.0016
## [691,]   -0.003750842577  0.351227021       0.0000       0.0000 0.0016
## [692,]    0.000000000000  0.000000000       0.0000       0.0000 0.0000
## [693,]   -0.004910211972  0.250846461       0.0000       0.0000 0.0024
## [694,]   -0.004270543288  0.154016171       0.0000       0.0000 0.0008
## [695,]   -0.008473216475  0.315276715       0.0000       0.0000 0.0012
## [696,]   -0.010404344443  0.496529060       0.0000       0.0000 0.0008
## [697,]   -0.005884076542  0.294203827       0.0000       0.0000 0.0004
## [698,]   -0.012668341643  0.735272199       0.0000       0.0000 0.0016
## [699,]    0.030471096026  1.625674083       0.0000       0.0000 0.0008
## [700,]   -0.008879136980  0.836524582       0.0000       0.0000 0.0024
## [701,]    0.014651838059  0.795334575       0.0000       0.0000 0.0012
## [702,]   -0.079998999029  2.515463052       0.0000       0.0000 0.0020
## [703,]    1.649691275482 13.065987190       0.0000       0.0000 0.0188
## [704,]   -0.014540488584  1.046134987       0.0000       0.0000 0.0024
## [705,]   -0.006903006355  0.298562290       0.0000       0.0000 0.0008
## [706,]   -0.004135288899  0.150384461       0.0000       0.0000 0.0008
## [707,]    0.063585429958  1.610385562       0.0000       0.0000 0.0020
## [708,]   -0.039278016278  0.950504640       0.0000       0.0000 0.0028
## [709,]   -0.002925792351  0.385587234       0.0000       0.0000 0.0020
## [710,]   -0.007347582265  0.276866945       0.0000       0.0000 0.0012

4.4.4 Predict fitted values for each individual

pred.npb3 <- predict(fit.npb3)
fittedvals3 <- pred.npb3$fitted.vals

4.4.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals3, Y)
abline(a = 0, b = 1, col = "red")

4.5 Fit the NPB model without ozone and without temperature

Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone or temperature just to see if something else pops up instead.

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "latina_re"    
##  [5] "black_re"      "other_re"      "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
# fit.npb4 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2,3)], Y = Y, W = W.scaled2,
#                 scaleY = TRUE,
#                 priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb4, file = here::here("Results", "NPB_Birth_Weight_v4.4.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4.4.rdata"))
npb.sum4 <- summary(fit.npb4)

4.5.1 First, main effect regression coefficients with PIPs

rownames(npb.sum4$main.effects) <- colnames(X.scaled[,-c(2,3)])
npb.sum4$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                 0.40578368  6.238661   -10.652441    16.447532 0.2812
## pct_tree_cover          0.28421997  5.425274   -10.914631    15.160063 0.2832
## pct_impervious         -0.70674846  6.141713   -16.346584    10.648090 0.2796
## mean_aadt_intensity     0.55679440  5.408335    -9.936939    16.097481 0.2692
## dist_m_tri              0.08654166  6.150674   -11.611509    15.084605 0.2744
## dist_m_npl              0.93564634  6.284110    -9.171112    18.764155 0.2744
## dist_m_waste_site       4.16087038 12.119108    -6.881603    43.982400 0.3464
## dist_m_major_emit       0.86835459  5.777090    -8.191580    19.314876 0.2712
## dist_m_cafo            -1.33503413 15.246851   -29.651063    17.365238 0.3132
## dist_m_mine_well       -1.80077181  8.251401   -26.867929     8.701758 0.3168
## cvd_rate_adj           -0.84099481  6.469780   -17.481338    10.128433 0.2792
## res_rate_adj           -1.64087938  7.134150   -22.954125     6.281887 0.2880
## violent_crime_rate      0.05864854  5.334227   -10.418866    12.035443 0.2572
## property_crime_rate    -1.02677057  5.777023   -15.971722     9.167573 0.2788
## pct_less_hs            -0.66943978  6.683276   -17.264286    11.520644 0.2820
## pct_unemp              -7.11959173 16.077084   -58.746261     3.884256 0.3960
## pct_limited_eng        -0.56072140  5.524495   -13.458147     9.608179 0.2620
## pct_hh_pov             -0.42073538  6.302446   -13.637270    10.841550 0.2684
## pct_poc                -0.13404666  5.949404   -11.946607    12.252535 0.2780

4.5.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum4$interactions
##        Posterior Mean         SD 95% CI Lower 95% CI Upper    PIP
##   [1,] -0.02065446795  0.6015368            0            0 0.0056
##   [2,] -0.02341076319  0.8228203            0            0 0.0072
##   [3,]  0.02485529396  0.7418679            0            0 0.0048
##   [4,] -0.01496215309  0.6473938            0            0 0.0080
##   [5,] -0.00482031233  0.4670947            0            0 0.0044
##   [6,] -0.02469669327  0.6503256            0            0 0.0112
##   [7,] -0.05258158697  0.8446635            0            0 0.0100
##   [8,] -0.01059384634  0.2747343            0            0 0.0052
##   [9,] -0.03631715034  0.7110691            0            0 0.0068
##  [10,] -0.00888547190  0.4987186            0            0 0.0072
##  [11,]  0.00309019847  0.9441684            0            0 0.0088
##  [12,] -0.02612465942  0.5632420            0            0 0.0076
##  [13,] -0.02465078038  0.5384283            0            0 0.0084
##  [14,] -0.03828614499  1.0866126            0            0 0.0080
##  [15,]  0.00137577824  0.4276096            0            0 0.0056
##  [16,] -0.07024542069  1.4551794            0            0 0.0088
##  [17,] -0.02147735667  0.6241154            0            0 0.0076
##  [18,] -0.01496887365  0.5962158            0            0 0.0096
##  [19,]  0.00034923212  0.5038999            0            0 0.0068
##  [20,] -0.00849113339  0.6176878            0            0 0.0072
##  [21,] -0.01644835308  0.3685240            0            0 0.0072
##  [22,]  0.00939165483  0.3767220            0            0 0.0048
##  [23,] -0.00882311763  0.2478394            0            0 0.0056
##  [24,]  0.02350289386  0.8159647            0            0 0.0092
##  [25,] -0.02887065157  0.6933436            0            0 0.0056
##  [26,] -0.06457714471  1.2314826            0            0 0.0100
##  [27,]  0.00484344233  0.3030374            0            0 0.0048
##  [28,] -0.01605947641  0.7122592            0            0 0.0068
##  [29,] -0.02858913398  0.5816460            0            0 0.0052
##  [30,] -0.01756085774  0.4066001            0            0 0.0052
##  [31,] -0.02084713198  0.6446724            0            0 0.0044
##  [32,] -0.00925948967  0.9450859            0            0 0.0056
##  [33,] -0.00423364159  0.4182012            0            0 0.0076
##  [34,]  0.03022255470  1.1236425            0            0 0.0080
##  [35,] -0.00835636462  0.4274997            0            0 0.0088
##  [36,]  0.01401058768  0.7505233            0            0 0.0080
##  [37,]  0.03756279610  1.0257230            0            0 0.0080
##  [38,]  0.00130939493  0.1646558            0            0 0.0032
##  [39,] -0.00233030888  0.8668748            0            0 0.0088
##  [40,] -0.02639539710  0.5346244            0            0 0.0084
##  [41,] -0.01628525699  0.5438343            0            0 0.0088
##  [42,] -0.00592696294  0.2232116            0            0 0.0052
##  [43,] -0.00663602300  0.6183788            0            0 0.0068
##  [44,] -0.04792206879  0.8730535            0            0 0.0080
##  [45,] -0.00922201832  0.4621741            0            0 0.0080
##  [46,] -0.01589233420  0.4759240            0            0 0.0068
##  [47,] -0.00214994390  0.4088931            0            0 0.0068
##  [48,] -0.03141014339  0.6370374            0            0 0.0068
##  [49,] -0.00594966491  0.6956222            0            0 0.0076
##  [50,] -0.02466581727  0.9043653            0            0 0.0072
##  [51,] -0.00595767439  0.3282689            0            0 0.0068
##  [52,]  0.05728879704  1.5234056            0            0 0.0092
##  [53,] -0.00611425681  0.6199917            0            0 0.0060
##  [54,]  0.00997451760  0.4412287            0            0 0.0064
##  [55,]  0.06464651684  1.5354598            0            0 0.0092
##  [56,] -0.02385158752  0.8825710            0            0 0.0080
##  [57,] -0.06318203102  1.2263254            0            0 0.0088
##  [58,] -0.03002425122  0.9566229            0            0 0.0092
##  [59,] -0.02329722502  0.6443755            0            0 0.0048
##  [60,] -0.01840088140  0.4712620            0            0 0.0064
##  [61,] -0.01353423412  0.3695652            0            0 0.0084
##  [62,]  0.01293726341  0.8087230            0            0 0.0092
##  [63,] -0.00084032418  0.8772134            0            0 0.0060
##  [64,] -0.02526438827  0.4437155            0            0 0.0112
##  [65,]  0.00258408702  0.4313218            0            0 0.0060
##  [66,]  0.05193732841  1.0283016            0            0 0.0080
##  [67,] -0.00504686581  0.2839564            0            0 0.0080
##  [68,] -0.00289700914  0.2015575            0            0 0.0048
##  [69,] -0.00233572180  0.5217469            0            0 0.0080
##  [70,]  0.00970885728  0.4283611            0            0 0.0072
##  [71,] -0.00592771137  0.5287096            0            0 0.0104
##  [72,]  0.00512369618  0.2455939            0            0 0.0056
##  [73,] -0.00375340316  0.5311847            0            0 0.0068
##  [74,]  0.00642854820  0.4920710            0            0 0.0056
##  [75,] -0.00134992785  0.6483244            0            0 0.0076
##  [76,] -0.00379124546  0.5979684            0            0 0.0080
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## [646,] -0.03503125691  1.0448565            0            0 0.0096
## [647,]  0.03040614981  1.5875663            0            0 0.0064
## [648,] -0.02683469105  0.5904054            0            0 0.0092
## [649,] -0.01088160897  1.1736270            0            0 0.0080
## [650,] -0.02058211611  0.4677316            0            0 0.0056
## [651,]  0.04283203256  1.8765122            0            0 0.0124
## [652,] -0.00126246304  0.6584181            0            0 0.0076
## [653,] -0.01231690436  0.5908343            0            0 0.0064
## [654,]  0.00284019897  0.8361066            0            0 0.0060
## [655,] -0.01345065152  2.1896876            0            0 0.0096
## [656,]  0.01076277742  0.6625391            0            0 0.0056
## [657,] -0.32885065034  5.0224256            0            0 0.0136
## [658,]  0.82852899629  9.0863564            0            0 0.0152
## [659,] -0.04682066314  1.1746644            0            0 0.0068
## [660,] -0.02368944365  0.8336448            0            0 0.0088
## [661,] -0.02464555303  0.9569493            0            0 0.0076
## [662,]  0.01780628346  1.3442671            0            0 0.0076
## [663,] -0.06544736531  1.1296142            0            0 0.0092
## [664,] -0.03617788916  0.7566387            0            0 0.0088
## [665,] -0.04996283617  1.5369428            0            0 0.0072

4.5.4 Predict fitted values for each individual

pred.npb4 <- predict(fit.npb4)
fittedvals4 <- pred.npb4$fitted.vals

4.5.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals4, Y)
abline(a = 0, b = 1, col = "red")

5 Linear models for each predictor

5.1 Screening the exposures

Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.

The standard deviation of the mean_o3 variable is 3.06 ppb

lm_results <- data.frame()

for(i in 1:length(colnames(X.scaled))) {
  lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
  names(lm_df)[2] <- colnames(X.scaled)[i]
  
  ad_lm <- lm(birth_weight ~ ., data = lm_df)
  
  temp <- data.frame(exp = colnames(X.scaled)[i],
                     beta = summary(ad_lm)$coefficients[2,1],
                     beta.se = summary(ad_lm)$coefficients[2,2],
                     p.value = summary(ad_lm)$coefficients[2,4])
  temp$lcl <- temp$beta - 1.96*temp$beta.se
  temp$ucl <- temp$beta + 1.96*temp$beta.se
  lm_results <- bind_rows(lm_results, temp)
  rm(temp)
}

lm_results
write_csv(lm_results, here::here("Results", "LM_Effects_Birth_Weight_v4.csv"))

6 Linear model with the ozone and temperature predictors

The standard deviation of the mean_o3 variable is 3.06 ppb The standard deviation of the mean_temp variable is 4.54 degrees F

lm_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(lm_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "latina_re"     "black_re"     
##  [9] "other_re"      "ed_no_hs"      "ed_hs"         "ed_aa"        
## [13] "ed_4yr"        "low_bmi"       "ovwt_bmi"      "obese_bmi"    
## [17] "concep_spring" "concep_summer" "concep_fall"   "concep_2010"  
## [21] "concep_2011"   "concep_2012"   "concep_2013"   "maternal_age" 
## [25] "any_smoker"    "smokeSH"       "mean_cpss"     "mean_epsd"    
## [29] "male"
#names(lm_df)[2] <- "mean_o3"

head(lm_df)
bw_lm <- lm(birth_weight ~ mean_o3 + mean_temp + mean_o3*mean_temp +
              lat + lon + lat_lon_int +
              latina_re + black_re + other_re + 
              ed_no_hs + ed_hs + ed_aa + ed_4yr + 
              low_bmi + ovwt_bmi + obese_bmi + 
              concep_spring + concep_summer + concep_fall +
              concep_2010 + concep_2011 + concep_2012 + concep_2013 +
              maternal_age + any_smoker + smokeSH + 
              mean_cpss + mean_epsd + male,
              data = lm_df)

summary(bw_lm)
## 
## Call:
## lm(formula = birth_weight ~ mean_o3 + mean_temp + mean_o3 * mean_temp + 
##     lat + lon + lat_lon_int + latina_re + black_re + other_re + 
##     ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + 
##     obese_bmi + concep_spring + concep_summer + concep_fall + 
##     concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age + 
##     any_smoker + smokeSH + mean_cpss + mean_epsd + male, data = lm_df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1949.66  -299.30    32.42   320.13  1391.98 
## 
## Coefficients:
##                    Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)        2951.708    484.042   6.098        0.00000000162 ***
## mean_o3            -111.550     53.782  -2.074              0.03836 *  
## mean_temp            84.775     53.297   1.591              0.11206    
## lat                  39.445  17353.487   0.002              0.99819    
## lon                   3.946   8171.897   0.000              0.99961    
## lat_lon_int          51.064  20965.561   0.002              0.99806    
## latina_re          -101.910     46.323  -2.200              0.02807 *  
## black_re           -291.040     49.984  -5.823        0.00000000815 ***
## other_re            -98.104     67.067  -1.463              0.14389    
## ed_no_hs            158.566     75.327   2.105              0.03558 *  
## ed_hs               135.453     67.217   2.015              0.04420 *  
## ed_aa                76.692     59.249   1.294              0.19587    
## ed_4yr               88.459     49.852   1.774              0.07634 .  
## low_bmi             -82.355     90.617  -0.909              0.36369    
## ovwt_bmi             42.942     39.431   1.089              0.27644    
## obese_bmi           122.909     44.537   2.760              0.00591 ** 
## concep_spring      -151.372     57.096  -2.651              0.00817 ** 
## concep_summer       -84.097     74.042  -1.136              0.25635    
## concep_fall           2.543     70.975   0.036              0.97143    
## concep_2010         307.856    485.074   0.635              0.52582    
## concep_2011         300.403    485.844   0.618              0.53653    
## concep_2012         394.746    487.939   0.809              0.41873    
## concep_2013         380.787    485.067   0.785              0.43266    
## maternal_age         57.432     21.591   2.660              0.00796 ** 
## any_smoker         -151.703     62.418  -2.430              0.01528 *  
## smokeSH             -74.770     43.616  -1.714              0.08684 .  
## mean_cpss             3.557     19.365   0.184              0.85430    
## mean_epsd           -46.277     19.680  -2.352              0.01892 *  
## male                174.141     31.857   5.466        0.00000006010 ***
## mean_o3:mean_temp  -151.446     16.515  -9.170 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 470.2 on 867 degrees of freedom
## Multiple R-squared:  0.2284, Adjusted R-squared:  0.2025 
## F-statistic: 8.847 on 29 and 867 DF,  p-value: < 0.00000000000000022
plot(bw_lm)
## Warning: not plotting observations with leverage one:
##   1

7 Try a GAM with the ozone and temperature predictor

The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone and temperature to see about potential nonlinear effects

The mean and standard deviation of the mean_o3 variable are 47.96 (3.06) ppb The mean and standard deviation of the mean_temp variable is 52.58 (4.54) degrees F

library(mgcv)
## Loading required package: nlme
## 
## Attaching package: 'nlme'
## The following object is masked from 'package:dplyr':
## 
##     collapse
## This is mgcv 1.8-34. For overview type 'help("mgcv-package")'.
library(tidymv)

gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "latina_re"     "black_re"     
##  [9] "other_re"      "ed_no_hs"      "ed_hs"         "ed_aa"        
## [13] "ed_4yr"        "low_bmi"       "ovwt_bmi"      "obese_bmi"    
## [17] "concep_spring" "concep_summer" "concep_fall"   "concep_2010"  
## [21] "concep_2011"   "concep_2012"   "concep_2013"   "maternal_age" 
## [25] "any_smoker"    "smokeSH"       "mean_cpss"     "mean_epsd"    
## [29] "male"
#names(gam_df)[2] <- "mean_o3"

head(gam_df)
bw_gam <- gam(birth_weight ~ s(mean_o3, mean_temp) +
                lat + lon + lat_lon_int +
                latina_re + black_re + other_re + 
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df, method = "REML")
gam.check(bw_gam)

## 
## Method: REML   Optimizer: outer newton
## full convergence after 5 iterations.
## Gradient range [-0.003901862,0.0002318709]
## (score 6612.104 & scale 198536.5).
## Hessian positive definite, eigenvalue range [6.271652,434.1997].
## Model rank =  56 / 56 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                        k'  edf k-index p-value
## s(mean_o3,mean_temp) 29.0 20.3    1.02    0.73
summary(bw_gam)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male
## 
## Parametric coefficients:
##                Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)    2672.485    463.780   5.762 0.00000001159 ***
## lat            1969.493  16669.709   0.118       0.90598    
## lon            -899.973   7850.164  -0.115       0.90875    
## lat_lon_int    2378.919  20139.472   0.118       0.90600    
## latina_re       -93.390     44.358  -2.105       0.03555 *  
## black_re       -282.806     47.713  -5.927 0.00000000447 ***
## other_re        -84.252     64.088  -1.315       0.18899    
## ed_no_hs        127.350     72.093   1.766       0.07768 .  
## ed_hs           105.756     64.554   1.638       0.10174    
## ed_aa            73.939     56.623   1.306       0.19197    
## ed_4yr           77.556     47.667   1.627       0.10410    
## low_bmi        -125.792     86.718  -1.451       0.14727    
## ovwt_bmi         54.344     37.778   1.439       0.15066    
## obese_bmi       107.672     42.678   2.523       0.01182 *  
## concep_spring  -115.526     62.210  -1.857       0.06365 .  
## concep_summer  -212.023     91.687  -2.312       0.02099 *  
## concep_fall     -78.197     89.775  -0.871       0.38398    
## concep_2010     535.014    467.861   1.144       0.25314    
## concep_2011     475.483    468.750   1.014       0.31070    
## concep_2012     643.518    470.386   1.368       0.17165    
## concep_2013     582.557    468.024   1.245       0.21358    
## maternal_age     60.560     20.658   2.932       0.00346 ** 
## any_smoker     -154.503     59.686  -2.589       0.00980 ** 
## smokeSH         -63.289     41.579  -1.522       0.12835    
## mean_cpss         2.203     18.589   0.119       0.90568    
## mean_epsd       -45.229     18.829  -2.402       0.01651 *  
## male            157.454     30.433   5.174 0.00000028641 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                       edf Ref.df    F             p-value    
## s(mean_o3,mean_temp) 20.3  25.08 7.64 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.284   Deviance explained = 32.1%
## -REML = 6612.1  Scale est. = 1.9854e+05  n = 897
save(gam_df, bw_gam, file = here::here("Results", "BW_GAM_v4.rdata"))
library(mgcViz)
## Loading required package: qgam
## Loading required package: rgl
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
## Registered S3 method overwritten by 'mgcViz':
##   method from  
##   +.gg   GGally
## 
## Attaching package: 'mgcViz'
## The following objects are masked from 'package:stats':
## 
##     qqline, qqnorm, qqplot
gam_b <- getViz(bw_gam)
plot(sm(gam_b, 1)) + 
  l_fitRaster() + l_fitContour() + l_points() +
  labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
  guides(fill=guide_legend(title="Change in\nbirth weight (g)")) +
ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_v4.jpeg"),
       device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)  

8 GAM Sensitivity Analysis

The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.

Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 2.5% of data and just use the middle 95%.

library(mgcv)

gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "latina_re"     "black_re"     
##  [9] "other_re"      "ed_no_hs"      "ed_hs"         "ed_aa"        
## [13] "ed_4yr"        "low_bmi"       "ovwt_bmi"      "obese_bmi"    
## [17] "concep_spring" "concep_summer" "concep_fall"   "concep_2010"  
## [21] "concep_2011"   "concep_2012"   "concep_2013"   "maternal_age" 
## [25] "any_smoker"    "smokeSH"       "mean_cpss"     "mean_epsd"    
## [29] "male"
head(gam_df)
gam_df2 <- gam_df %>%
  filter(mean_o3 > -2 & mean_o3 < 2) %>%
  filter(mean_temp > -2 & mean_temp < 2)
hist(gam_df2$mean_o3)

hist(gam_df2$mean_temp)

bw_gam2 <- gam(birth_weight ~ s(mean_o3, mean_temp) + 
                lat + lon + lat_lon_int +
                latina_re + black_re + other_re + 
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df2, method = "REML")
gam.check(bw_gam2)

## 
## Method: REML   Optimizer: outer newton
## full convergence after 6 iterations.
## Gradient range [-0.00000008175124,0.000000001043013]
## (score 6455.826 & scale 197464).
## Hessian positive definite, eigenvalue range [2.947887,424.5697].
## Model rank =  56 / 56 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                        k'  edf k-index p-value
## s(mean_o3,mean_temp) 29.0 12.8    1.02    0.69
summary(bw_gam2)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male
## 
## Parametric coefficients:
##               Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)    2757.43     461.13   5.980 0.00000000331 ***
## lat            6394.80   16840.59   0.380       0.70425    
## lon           -2991.04    7930.73  -0.377       0.70616    
## lat_lon_int    7724.85   20346.00   0.380       0.70428    
## latina_re      -113.84      44.46  -2.561       0.01062 *  
## black_re       -288.02      47.86  -6.018 0.00000000264 ***
## other_re        -91.52      64.36  -1.422       0.15543    
## ed_no_hs        150.48      72.28   2.082       0.03766 *  
## ed_hs           125.31      64.64   1.939       0.05287 .  
## ed_aa            91.76      56.90   1.613       0.10722    
## ed_4yr           86.82      47.99   1.809       0.07081 .  
## low_bmi        -123.30      86.28  -1.429       0.15337    
## ovwt_bmi         49.69      38.06   1.306       0.19205    
## obese_bmi       101.48      42.97   2.362       0.01840 *  
## concep_spring   -90.04      61.27  -1.470       0.14203    
## concep_summer  -167.34      87.73  -1.907       0.05680 .  
## concep_fall     -58.98      85.36  -0.691       0.48980    
## concep_2010     463.35     464.50   0.998       0.31879    
## concep_2011     407.37     465.27   0.876       0.38152    
## concep_2012     543.76     467.05   1.164       0.24466    
## concep_2013     514.05     464.70   1.106       0.26896    
## maternal_age     61.12      20.74   2.947       0.00329 ** 
## any_smoker     -162.02      59.74  -2.712       0.00683 ** 
## smokeSH         -78.62      41.90  -1.876       0.06099 .  
## mean_cpss         5.43      18.68   0.291       0.77134    
## mean_epsd       -46.95      18.91  -2.483       0.01322 *  
## male            148.06      30.64   4.832 0.00000160761 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                        edf Ref.df     F  p-value    
## s(mean_o3,mean_temp) 12.84  17.44 2.622 0.000321 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.181   Deviance explained = 21.7%
## -REML = 6455.8  Scale est. = 1.9746e+05  n = 878
save(gam_df2, bw_gam2, file = here::here("Results", "BW_GAM_Sensitivity_v4.rdata"))
library(mgcViz)
gam_b2 <- getViz(bw_gam2)
plot(sm(gam_b2, 1)) + 
  l_fitRaster() + l_fitContour() + l_points() +
  labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
  guides(fill=guide_legend(title="Change in\nbirth weight (g)"))

ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_Sensitivity_v4.jpeg"),
       device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)